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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="diraf.html#NM2">AffinPlane</a>;<br/><b>let </b><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> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>11</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





















<b>assume </b><b>that </b><br/><a NAME="E1:27"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>11</sub></font>
 <b>and </b><br/><a NAME="E2:27"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> )
 <b>and </b><br/><a NAME="E3:27"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="aff_2.html#NR7" target="_self">satisfies_TDES</a> 
 <b>and </b><br/><a NAME="E4:27"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> )
 <b>and </b><br/><a NAME="E5:27"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>and </b><br/><a NAME="E6:27"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font> )
 ;<br/>

<a NAME="E7:27"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">c<sub>10</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp; <font color="Maroon">c<sub>11</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a>  )
 
<b>by </b><i><a class="txt" href="homothet.html#E1:27"><i><font color="Green">E28</font></i></a>, <a class="ref" href="aff_1.html#T50">AFF_1:50</a></i>;<br/>
<div><i><font color="Green">E35</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:27_1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font>
 ;<br/><a NAME="E2:27_1"/>
<font color="Maroon">c<sub>10</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E7:27"><i><font color="Green">E34</font></i></a>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/><b>hence </b><a NAME="E3:27_1"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E2:27"><i><font color="Green">E29</font></i></a>, <a class="txt" href="homothet.html#E4:27"><i><font color="Green">E31</font></i></a>, <a class="txt" href="homothet.html#E1:27_1"><i><font color="Green">E36</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:27_2"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>11</sub></font>
 ;<br/><a NAME="E2:27_2"/><b>then </b><i><font color="Green">E37</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="homothet.html#E1:27"><i><font color="Green">E28</font></i></a>, <a class="txt" href="homothet.html#E2:27"><i><font color="Green">E29</font></i></a>, <a class="txt" href="homothet.html#E4:27"><i><font color="Green">E31</font></i></a>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/><a NAME="E3:27_2"/><i><font color="Green">E38</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>9</sub></font> )
 <b>by </b><i><a class="txt" href="homothet.html#E1:27"><i><font color="Green">E28</font></i></a>, <a class="txt" href="homothet.html#E2:27"><i><font color="Green">E29</font></i></a>, <a class="txt" href="homothet.html#E4:27"><i><font color="Green">E31</font></i></a>, <a class="txt" href="homothet.html#E1:27_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/><b>set </b><font color="Maroon">c<sub>12</sub></font> =  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>;<br/><b>set </b><font color="Maroon">c<sub>13</sub></font> =  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>;<br/><b>set </b><font color="Maroon">c<sub>14</sub></font> =  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font>;<br/><b>set </b><font color="Maroon">c<sub>15</sub></font> =  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>;<br/><b>set </b><font color="Maroon">c<sub>16</sub></font> =  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font>;<br/><b>set </b><font color="Maroon">c<sub>17</sub></font> =  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>9</sub></font>;<br/><b>set </b><font color="Maroon">c<sub>18</sub></font> =  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>9</sub></font>;<br/><b>set </b><font color="Maroon">c<sub>19</sub></font> =  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font>;<br/><a NAME="E4:27_2"/><i><font color="Green">E39</font></i>: 
(  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp;  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp;  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp;  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp;  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp;  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp;  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp;  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a>  )
 <b>by </b><i><a class="txt" href="homothet.html#E2:27_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="homothet.html#E3:27_2"><i><font color="Green">E38</font></i></a>, <a class="ref" href="aff_1.html#D3">AFF_1:def 3</a></i>;<br/><a NAME="E5:27_2"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T26">AFF_1:26</a></i>;<br/><a NAME="E6:27_2"/><i><font color="Green">E41</font></i>: 
(  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="aff_1.html#R4">//</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp;  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="aff_1.html#R4">//</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>9</sub></font> &amp;  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="aff_1.html#R4">//</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font> )
 <b>by </b><i><a class="txt" href="homothet.html#E6:27"><i><font color="Green">E33</font></i></a>, <a class="txt" href="homothet.html#E2:27_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="homothet.html#E3:27_2"><i><font color="Green">E38</font></i></a>, <a class="ref" href="aff_1.html#T51">AFF_1:51</a></i>;<br/><a NAME="E7:27_2"/><i><font color="Green">E42</font></i>: 
( not <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; not <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; not <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; not <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; not <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; not <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> )
 <b>by </b><i><a class="txt" href="homothet.html#E1:27"><i><font color="Green">E28</font></i></a>, <a class="txt" href="homothet.html#E2:27"><i><font color="Green">E29</font></i></a>, <a class="txt" href="homothet.html#E4:27"><i><font color="Green">E31</font></i></a>, <a class="txt" href="homothet.html#E1:27_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/><a NAME="E8:27_2"/><i><font color="Green">E43</font></i>: 
(  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>10</sub></font> &amp;  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>10</sub></font> &amp;  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>10</sub></font> &amp;  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>10</sub></font> &amp;  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>10</sub></font> &amp;  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>10</sub></font> &amp;  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>10</sub></font> &amp;  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>10</sub></font> &amp;  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>11</sub></font> &amp;  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>11</sub></font> &amp;  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>11</sub></font> &amp;  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>11</sub></font> &amp;  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>11</sub></font> &amp;  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>11</sub></font> &amp;  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>11</sub></font> &amp;  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>11</sub></font> )
 <b>by </b><i><a class="txt" href="homothet.html#E1:27"><i><font color="Green">E28</font></i></a>, <a class="txt" href="homothet.html#E2:27"><i><font color="Green">E29</font></i></a>, <a class="txt" href="homothet.html#E4:27"><i><font color="Green">E31</font></i></a>, <a class="txt" href="homothet.html#E1:27_2"><i><font color="Green">E36</font></i></a>, <a class="txt" href="homothet.html#E5:27_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/><a NAME="E9:27_2"/><i><font color="Green">E44</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="txt" href="homothet.html#E2:27"><i><font color="Green">E29</font></i></a>, <a class="txt" href="homothet.html#E4:27"><i><font color="Green">E31</font></i></a>, <a class="txt" href="homothet.html#E7:27"><i><font color="Green">E34</font></i></a>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/><div><i><font color="Green">E45</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="27_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:27_2_1"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>(  <a href="aff_1.html#R1">LIN</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>3</sub></font> )
 ;<br/><b>then consider </b><font color="Maroon">c<sub>20</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:27_2_1"/><i><font color="Green">E46</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>20</sub></font> &amp; <font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> )
 <b>by </b><i><a class="txt" href="homothet.html#E2:27_2"><i><font color="Green">E37</font></i></a>, <a class="ref" href="translac.html#T2">TRANSLAC:2</a></i>;<br/><a NAME="E4:27_2_1"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E3:27_2_1"><i><font color="Green">E46</font></i></a>, <a class="ref" href="aff_1.html#D2">AFF_1:def 2</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>21</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E6:27_2_1"/><i><font color="Green">E48</font></i>: 
( <font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>21</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>21</sub></font> )
 <b>by </b><i><a class="txt" href="homothet.html#E7:27"><i><font color="Green">E34</font></i></a>, <a class="ref" href="aff_1.html#T63">AFF_1:63</a></i>;<br/><a NAME="E7:27_2_1"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>21</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a> 
 <b>by </b><i><a class="txt" href="homothet.html#E6:27_2_1"><i><font color="Green">E48</font></i></a>, <a class="ref" href="aff_1.html#T50">AFF_1:50</a></i>;<br/><a NAME="E8:27_2_1"/>
not  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>21</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_2_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:27_2_1_1"/>
 <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>21</sub></font>
 ;<br/>

<a NAME="E2:27_2_1_1"/><b>then </b>
 <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>21</sub></font>
 
<b>by </b><i><a class="txt" href="homothet.html#E6:27_2"><i><font color="Green">E41</font></i></a>, <a class="ref" href="aff_1.html#T58">AFF_1:58</a></i>;<br/>
<a NAME="E3:27_2_1_1"/><b>then </b>
 <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="homothet.html#E6:27_2_1"><i><font color="Green">E48</font></i></a>, <a class="ref" href="aff_1.html#T58">AFF_1:58</a></i>;<br/>
<b>hence </b><a NAME="E4:27_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="homothet.html#E2:27"><i><font color="Green">E29</font></i></a>, <a class="txt" href="homothet.html#E5:27_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="homothet.html#E8:27_2"><i><font color="Green">E43</font></i></a>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon">c<sub>22</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E10:27_2_1"/><i><font color="Green">E50</font></i>: 
( <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>21</sub></font> )
 <b>by </b><i><a class="txt" href="homothet.html#E4:27_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="homothet.html#E7:27_2_1"><i><font color="Green">E49</font></i></a>, <a class="ref" href="aff_1.html#T72">AFF_1:72</a></i>;<br/><a NAME="E11:27_2_1"/>
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>22</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>21</sub></font> &amp; <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>21</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>21</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>21</sub></font> )
 <b>by </b><i><a class="txt" href="homothet.html#E1:27"><i><font color="Green">E28</font></i></a>, <a class="txt" href="homothet.html#E2:27"><i><font color="Green">E29</font></i></a>, <a class="txt" href="homothet.html#E4:27"><i><font color="Green">E31</font></i></a>, <a class="txt" href="homothet.html#E7:27"><i><font color="Green">E34</font></i></a>, <a class="txt" href="homothet.html#E1:27_2"><i><font color="Green">E36</font></i></a>, <a class="txt" href="homothet.html#E4:27_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="homothet.html#E5:27_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="homothet.html#E6:27_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="homothet.html#E8:27_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="homothet.html#E3:27_2_1"><i><font color="Green">E46</font></i></a>, <a class="txt" href="homothet.html#E4:27_2_1"><i><font color="Green">E47</font></i></a>, <a class="txt" href="homothet.html#E6:27_2_1"><i><font color="Green">E48</font></i></a>, <a class="txt" href="homothet.html#E10:27_2_1"><i><font color="Green">E50</font></i></a>, <a class="ref" href="aff_1.html#T30">AFF_1:30</a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E12:27_2_1"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>20</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>22</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>21</sub></font> &amp; <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>21</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>21</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>21</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>10</sub></font> )
 <b>by </b><i><a class="txt" href="homothet.html#E2:27"><i><font color="Green">E29</font></i></a>, <a class="txt" href="homothet.html#E3:27"><i><font color="Green">E30</font></i></a>, <a class="txt" href="homothet.html#E4:27"><i><font color="Green">E31</font></i></a>, <a class="txt" href="homothet.html#E7:27"><i><font color="Green">E34</font></i></a>, <a class="txt" href="homothet.html#E4:27_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="homothet.html#E5:27_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="homothet.html#E6:27_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="homothet.html#E8:27_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="homothet.html#E3:27_2_1"><i><font color="Green">E46</font></i></a>, <a class="txt" href="homothet.html#E4:27_2_1"><i><font color="Green">E47</font></i></a>, <a class="txt" href="homothet.html#E4"><i><font color="Green">Lemma4</font></i></a>, <a class="ref" href="aff_1.html#T30">AFF_1:30</a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a>, <a class="ref" href="aff_1.html#T58">AFF_1:58</a></i>;<br/><a NAME="E13:27_2_1"/><b>then </b>
( <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>21</sub></font> &amp; <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>21</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>21</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>21</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>21</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>21</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>10</sub></font> )
 <b>by </b><i><a class="txt" href="homothet.html#E2:27"><i><font color="Green">E29</font></i></a>, <a class="txt" href="homothet.html#E3:27"><i><font color="Green">E30</font></i></a>, <a class="txt" href="homothet.html#E4:27"><i><font color="Green">E31</font></i></a>, <a class="txt" href="homothet.html#E7:27"><i><font color="Green">E34</font></i></a>, <a class="txt" href="homothet.html#E4:27_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="homothet.html#E5:27_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="homothet.html#E6:27_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="homothet.html#E8:27_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="homothet.html#E3:27_2_1"><i><font color="Green">E46</font></i></a>, <a class="txt" href="homothet.html#E4:27_2_1"><i><font color="Green">E47</font></i></a>, <a class="txt" href="homothet.html#E6:27_2_1"><i><font color="Green">E48</font></i></a>, <a class="txt" href="homothet.html#E10:27_2_1"><i><font color="Green">E50</font></i></a>, <a class="txt" href="homothet.html#E4"><i><font color="Green">Lemma4</font></i></a>, <a class="ref" href="aff_1.html#T30">AFF_1:30</a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><b>hence </b><a NAME="E14:27_2_1"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E3:27"><i><font color="Green">E30</font></i></a>, <a class="txt" href="homothet.html#E4"><i><font color="Green">Lemma4</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:27_2_2"/><i><font color="Green">E46</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds <br/>(  not  <a href="aff_1.html#R1">LIN</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font> or  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>2</sub></font> or  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>3</sub></font> or  not <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>3</sub></font> )
 ;<br/><div><i><font color="Green">E47</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="27_2_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:27_2_2_1"/><i><font color="Green">E48</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> )
 ;<br/><a NAME="E2:27_2_2_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E6:27"><i><font color="Green">E33</font></i></a>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E3:27_2_2_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E4:27_2_2_1"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E4:27"><i><font color="Green">E31</font></i></a>, <a class="txt" href="homothet.html#E7:27"><i><font color="Green">E34</font></i></a>, <a class="txt" href="homothet.html#E7:27_2"><i><font color="Green">E42</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><a NAME="E5:27_2_2_1"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E6:27"><i><font color="Green">E33</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E6:27_2_2_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E7:27_2_2_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E1:27_2_2_1"><i><font color="Green">E48</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><b>hence </b><a NAME="E8:27_2_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="homothet.html#E2:27"><i><font color="Green">E29</font></i></a>, <a class="txt" href="homothet.html#E5:27"><i><font color="Green">E32</font></i></a>, <a class="txt" href="homothet.html#E7:27"><i><font color="Green">E34</font></i></a>, <a class="txt" href="homothet.html#E7:27_2"><i><font color="Green">E42</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/></div><b>end;</b></div><div><i><font color="Green">E48</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="27_2_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:27_2_2_2"/><i><font color="Green">E49</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> )
 ;<br/><a NAME="E2:27_2_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E6:27"><i><font color="Green">E33</font></i></a>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E3:27_2_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E4:27_2_2_2"/><b>then </b>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E4:27"><i><font color="Green">E31</font></i></a>, <a class="txt" href="homothet.html#E7:27"><i><font color="Green">E34</font></i></a>, <a class="txt" href="homothet.html#E7:27_2"><i><font color="Green">E42</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><b>hence </b><a NAME="E5:27_2_2_2"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E1:27_2_2_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/></div><b>end;</b></div><div><i><font color="Green">E49</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="27_2_2_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:27_2_2_3"/><i><font color="Green">E50</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> )
 ;<br/><a NAME="E2:27_2_2_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E6:27"><i><font color="Green">E33</font></i></a>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E3:27_2_2_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E4:27_2_2_3"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E4:27"><i><font color="Green">E31</font></i></a>, <a class="txt" href="homothet.html#E7:27"><i><font color="Green">E34</font></i></a>, <a class="txt" href="homothet.html#E7:27_2"><i><font color="Green">E42</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><a NAME="E5:27_2_2_3"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E6:27"><i><font color="Green">E33</font></i></a>, <a class="txt" href="homothet.html#E1:27_2_2_3"><i><font color="Green">E50</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E6:27_2_2_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E7:27_2_2_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><b>hence </b><a NAME="E8:27_2_2_3"/>
contradiction
 <b>by </b><i><a class="txt" href="homothet.html#E2:27"><i><font color="Green">E29</font></i></a>, <a class="txt" href="homothet.html#E5:27"><i><font color="Green">E32</font></i></a>, <a class="txt" href="homothet.html#E7:27"><i><font color="Green">E34</font></i></a>, <a class="txt" href="homothet.html#E7:27_2"><i><font color="Green">E42</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_2_2_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:27_2_2_4"/><i><font color="Green">E50</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> )
 ;<br/><div><i><font color="Green">E51</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="27_2_2_4_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:27_2_2_4_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/><a NAME="E2:27_2_2_4_1"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E6:27"><i><font color="Green">E33</font></i></a>, <a class="txt" href="homothet.html#E1:27_2_2_4"><i><font color="Green">E50</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E3:27_2_2_4_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E4:27_2_2_4_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><b>hence </b><a NAME="E5:27_2_2_4_1"/>
contradiction
 <b>by </b><i><a class="txt" href="homothet.html#E2:27"><i><font color="Green">E29</font></i></a>, <a class="txt" href="homothet.html#E5:27"><i><font color="Green">E32</font></i></a>, <a class="txt" href="homothet.html#E7:27"><i><font color="Green">E34</font></i></a>, <a class="txt" href="homothet.html#E7:27_2"><i><font color="Green">E42</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_2_2_4_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:27_2_2_4_2"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/><a NAME="E2:27_2_2_4_2"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E6:27"><i><font color="Green">E33</font></i></a>, <a class="txt" href="homothet.html#E2:27_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="homothet.html#E1:27_2_2_4"><i><font color="Green">E50</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><a NAME="E3:27_2_2_4_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E4:27_2_2_4_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E5:27_2_2_4_2"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E4:27"><i><font color="Green">E31</font></i></a>, <a class="txt" href="homothet.html#E6:27"><i><font color="Green">E33</font></i></a>, <a class="txt" href="homothet.html#E7:27"><i><font color="Green">E34</font></i></a>, <a class="txt" href="homothet.html#E7:27_2"><i><font color="Green">E42</font></i></a>, <a class="txt" href="homothet.html#E1:27_2_2_4"><i><font color="Green">E50</font></i></a>, <a class="txt" href="homothet.html#E1:27_2_2_4_2"><i><font color="Green">E52</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><b>hence </b><a NAME="E6:27_2_2_4_2"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:27_2_2_4"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E5:27"><i><font color="Green">E32</font></i></a>, <a class="txt" href="homothet.html#E9:27_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="homothet.html#E1:27_2_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="homothet.html#E2:27_2_2_4"><i><font color="Green">E51</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E6:27_2_2"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E5:27"><i><font color="Green">E32</font></i></a>, <a class="txt" href="homothet.html#E9:27_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="homothet.html#E1:27_2_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="homothet.html#E2:27_2_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="homothet.html#E3:27_2_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="homothet.html#E4:27_2_2"><i><font color="Green">E49</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E12:27_2"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E10:27_2"><i><font color="Green">E45</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E10:27"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E8:27"><i><font color="Green">E35</font></i></a></i>;<br/>


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