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<b>let </b><font color="Maroon" title="c1">V</font> be   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">M</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="rusub_4.html#V2" title="RUSUB_4:attr.2">Affine</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</font>;<br/><b>let </b><font color="Maroon" title="c3">u</font>, <font color="Maroon" title="c4">v</font> be   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:19"/><i><font color="Green" title="E13">A1</font></i>: 
<font color="Maroon" title="c3">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">M</font>
 <b>and </b><br/><a NAME="E2:19"/><i><font color="Green" title="E14">A2</font></i>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">M</font>
 ;<br/>

<b>consider </b><font color="Maroon" title="c5">N1</font> being  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="rusub_4.html#V2" title="RUSUB_4:attr.2">Affine</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</font><b> such that </b><br/><a NAME="E4:19"/><i><font color="Green" title="E15">A3</font></i>: 
( <font color="Maroon" title="c5">N1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">M</font> <a href="rusub_5.html#K1" title="RUSUB_5:func.1">-</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">u</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <font color="Maroon" title="c2">M</font> <a href="rusub_5.html#R1" title="RUSUB_5:pred.1">is_parallel_to</a> <font color="Maroon" title="c5">N1</font> &amp; <font color="Maroon" title="c5">N1</font> is <a href="rusub_4.html#V3" title="RUSUB_4:attr.3">Subspace-like</a> )
 <b>by </b><i><a class="txt" href="rusub_5.html#E1:19"><i><font color="Green" title="E13">A1</font></i></a>, <a class="ref" href="rusub_5.html#T16" target="_self" title="RUSUB_5:th.16">Th16</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c6">N2</font> being  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="rusub_4.html#V2" title="RUSUB_4:attr.2">Affine</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</font><b> such that </b><br/><a NAME="E6:19"/><i><font color="Green" title="E16">A4</font></i>: 
( <font color="Maroon" title="c6">N2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">M</font> <a href="rusub_5.html#K1" title="RUSUB_5:func.1">-</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">v</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <font color="Maroon" title="c2">M</font> <a href="rusub_5.html#R1" title="RUSUB_5:pred.1">is_parallel_to</a> <font color="Maroon" title="c6">N2</font> &amp; <font color="Maroon" title="c6">N2</font> is <a href="rusub_4.html#V3" title="RUSUB_4:attr.3">Subspace-like</a> )
 <b>by </b><i><a class="txt" href="rusub_5.html#E2:19"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="rusub_5.html#T16" target="_self" title="RUSUB_5:th.16">Th16</a></i>;<br/>
<b>thus </b><a NAME="E7:19"/>
<font color="Maroon" title="c2">M</font> <a href="rusub_5.html#K1" title="RUSUB_5:func.1">-</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">v</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">M</font> <a href="rusub_5.html#K1" title="RUSUB_5:func.1">-</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">u</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>by </b><i><a class="txt" href="rusub_5.html#E4:19"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="rusub_5.html#E6:19"><i><font color="Green" title="E16">A4</font></i></a>, <a class="ref" href="rusub_5.html#T14" target="_self" title="RUSUB_5:th.14">Th14</a></i>;<br/>


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