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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> 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>3</sub></font> be   <a href="struct_0.html#NM2">Subset</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="E1:22"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="homothet.html#R1" target="_self">is_Sc</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E2:22"/><i><font color="Green">E24</font></i>: 
( <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="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; not <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<a NAME="E3:22"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="transgeo.html#NR10" target="_self">is_Col</a>  &amp; <font color="Maroon">c<sub>3</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> holds <br/><font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> ) )
 
<b>by </b><i><a class="txt" href="homothet.html#E1:22"><i><font color="Green">E23</font></i></a>, <a class="ref" href="homothet.html#D1" target="_self">Def1</a></i>;<br/>
<b>hence </b><a NAME="E4:22"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</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="homothet.html#E2:22"><i><font color="Green">E24</font></i></a>, <a class="ref" href="transgeo.html#T117">TRANSGEO:117</a></i>;<br/>


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