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<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="analoaf.html#NM1">OAffinSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</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>4</sub></font> be   <a href="funct_2.html#NM2">Permutation</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:74"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="transgeo.html#NR7" target="_self">is_Tr</a> 
 <b>and </b><br/><a NAME="E2:74"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E3:74"/><i><font color="Green">E46</font></i>: 
 <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E4:74"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="transgeo.html#NR6" target="_self">is_Dil</a> 
 
<b>by </b><i><a class="txt" href="transgeo.html#E1:74"><i><font color="Green">E44</font></i></a>, <a class="ref" href="transgeo.html#D9" target="_self">Def9</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>5</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="E6:74"/><i><font color="Green">E48</font></i>: 
not  <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="transgeo.html#E2:74"><i><font color="Green">E45</font></i></a>, <a class="ref" href="diraf.html#T43">DIRAF:43</a></i>;<br/>
<a NAME="E7:74"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="transgeo.html#E2:74"><i><font color="Green">E45</font></i></a>, <a class="ref" href="funct_1.html#T35">FUNCT_1:35</a></i>;<br/>
<a NAME="E8:74"/><b>then </b><i><font color="Green">E49</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>5</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>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="transgeo.html#E1:74"><i><font color="Green">E44</font></i></a>, <a class="ref" href="transgeo.html#D9" target="_self">Def9</a></i>;<br/>
<a NAME="E9:74"/><i><font color="Green">E50</font></i>: 
not  <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:74_1"/>
 <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:74_1"/><b>then </b>
(  <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp;  <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font> &amp;  <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="transgeo.html#E4:74"><i><font color="Green">E47</font></i></a>, <a class="ref" href="transgeo.html#T60" target="_self">Th60</a>, <a class="ref" href="diraf.html#T37">DIRAF:37</a></i>;<br/>
<b>hence </b><a NAME="E3:74_1"/>
contradiction
 <b>by </b><i><a class="txt" href="transgeo.html#E6:74"><i><font color="Green">E48</font></i></a>, <a class="txt" href="transgeo.html#E8:74"><i><font color="Green">E49</font></i></a>, <a class="ref" href="diraf.html#T38">DIRAF:38</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E10:74"/><i><font color="Green">E51</font></i>: 
not  <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:74_2"/><i><font color="Green">E52</font></i>: 
 <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E2:74_2"/>
(  <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp;  <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="transgeo.html#E3:74"><i><font color="Green">E46</font></i></a>, <a class="txt" href="transgeo.html#E4:74"><i><font color="Green">E47</font></i></a>, <a class="ref" href="transgeo.html#T60" target="_self">Th60</a>, <a class="ref" href="diraf.html#T37">DIRAF:37</a></i>;<br/>
<a NAME="E3:74_2"/><b>then </b>
 <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="transgeo.html#E2:74"><i><font color="Green">E45</font></i></a>, <a class="ref" href="diraf.html#T38">DIRAF:38</a></i>;<br/>
<a NAME="E4:74_2"/><b>then </b><i><font color="Green">E53</font></i>: 
(  <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="transgeo.html#E4:74"><i><font color="Green">E47</font></i></a>, <a class="ref" href="transgeo.html#T60" target="_self">Th60</a></i>;<br/>
<a NAME="E5:74_2"/><i><font color="Green">E54</font></i>: 
 <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="transgeo.html#E4:74"><i><font color="Green">E47</font></i></a>, <a class="txt" href="transgeo.html#E1:74_2"><i><font color="Green">E52</font></i></a>, <a class="ref" href="transgeo.html#T60" target="_self">Th60</a></i>;<br/>
<a NAME="E6:74_2"/>
 <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="diraf.html#T37">DIRAF:37</a></i>;<br/>
<a NAME="E7:74_2"/><b>then </b>
 <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="transgeo.html#E8:74"><i><font color="Green">E49</font></i></a>, <a class="txt" href="transgeo.html#E1:74_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="transgeo.html#E5:74_2"><i><font color="Green">E54</font></i></a>, <a class="ref" href="diraf.html#T38">DIRAF:38</a></i>;<br/>
<b>hence </b><a NAME="E8:74_2"/>
contradiction
 <b>by </b><i><a class="txt" href="transgeo.html#E6:74"><i><font color="Green">E48</font></i></a>, <a class="txt" href="transgeo.html#E8:74"><i><font color="Green">E49</font></i></a>, <a class="txt" href="transgeo.html#E4:74_2"><i><font color="Green">E53</font></i></a>, <a class="ref" href="diraf.html#T38">DIRAF:38</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E11:74"/><i><font color="Green">E52</font></i>: 
( <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="transgeo.html#E1:74"><i><font color="Green">E44</font></i></a>, <a class="txt" href="transgeo.html#E9:74"><i><font color="Green">E50</font></i></a>, <a class="txt" href="transgeo.html#E86"><i><font color="Green">Lemma42</font></i></a></i>;<br/>
<a NAME="E12:74"/>
( <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="transgeo.html#E1:74"><i><font color="Green">E44</font></i></a>, <a class="txt" href="transgeo.html#E10:74"><i><font color="Green">E51</font></i></a>, <a class="txt" href="transgeo.html#E86"><i><font color="Green">Lemma42</font></i></a></i>;<br/>
<b>hence </b><a NAME="E13:74"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="transgeo.html#E8:74"><i><font color="Green">E49</font></i></a>, <a class="txt" href="transgeo.html#E11:74"><i><font color="Green">E52</font></i></a>, <a class="ref" href="analoaf.html#D5">ANALOAF:def 5</a></i>;<br/>


</div>
