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<b>let </b><font color="Maroon">V</font> be   <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon">M</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="rusub_4.html#V2">Affine</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">u</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>, <font color="Maroon">v</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:19"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font>
 <b>and </b><br/><a NAME="E2:19"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">v</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font>
 ;<br/>

<b>consider </b><font color="Maroon">N1</font> being  non <a href="xboole_0.html#V1">empty</a> <a href="rusub_4.html#V2">Affine</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E4:19"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">N1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">M</font> <a href="rusub_5.html#K1" target="_self">-</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">u</font></span><a href="domain_1.html#K6">}</a></span> &amp; <font color="Maroon">M</font> <a href="rusub_5.html#R1" target="_self">is_parallel_to</a> <font color="Maroon">N1</font> &amp; <font color="Maroon">N1</font> is <a href="rusub_4.html#V3">Subspace-like</a> )
 <b>by </b><i>, </i>;<br/>
<b>consider </b><font color="Maroon">N2</font> being  non <a href="xboole_0.html#V1">empty</a> <a href="rusub_4.html#V2">Affine</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E6:19"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">N2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">M</font> <a href="rusub_5.html#K1" target="_self">-</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">v</font></span><a href="domain_1.html#K6">}</a></span> &amp; <font color="Maroon">M</font> <a href="rusub_5.html#R1" target="_self">is_parallel_to</a> <font color="Maroon">N2</font> &amp; <font color="Maroon">N2</font> is <a href="rusub_4.html#V3">Subspace-like</a> )
 <b>by </b><i>, </i>;<br/>
<b>thus </b><a NAME="E7:19"/>
<font color="Maroon">M</font> <a href="rusub_5.html#K1" target="_self">-</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">v</font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">M</font> <a href="rusub_5.html#K1" target="_self">-</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">u</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, , </i>;<br/>


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