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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="diraf.html#NM1">AffinSpace</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#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:16"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp; <font color="Maroon">c<sub>3</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a>  )
 ;<br/>

<a NAME="E2:16"/><b>then </b>
( (  <a href="afproj.html#K5" target="_self">LDir</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="afproj.html#K5" target="_self">LDir</a> <font color="Maroon">c<sub>3</sub></font> implies <font color="Maroon">c<sub>2</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>3</sub></font> ) &amp; ( <font color="Maroon">c<sub>2</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>3</sub></font> implies  <a href="afproj.html#K5" target="_self">LDir</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="afproj.html#K5" target="_self">LDir</a> <font color="Maroon">c<sub>3</sub></font> ) &amp; ( <font color="Maroon">c<sub>2</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>3</sub></font> implies <font color="Maroon">c<sub>2</sub></font> <a href="aff_4.html#R1">'||'</a> <font color="Maroon">c<sub>3</sub></font> ) &amp; ( <font color="Maroon">c<sub>2</sub></font> <a href="aff_4.html#R1">'||'</a> <font color="Maroon">c<sub>3</sub></font> implies <font color="Maroon">c<sub>2</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>3</sub></font> ) )
 
<b>by </b><i><a class="ref" href="afproj.html#T11" target="_self">Th11</a>, <a class="ref" href="aff_4.html#T40">AFF_4:40</a></i>;<br/>
<b>hence </b><a NAME="E3:16"/>
(  <a href="afproj.html#K5" target="_self">LDir</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="afproj.html#K5" target="_self">LDir</a> <font color="Maroon">c<sub>3</sub></font> iff <font color="Maroon">c<sub>2</sub></font> <a href="aff_4.html#R1">'||'</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>


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