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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">V1</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</font>;<br/>



<b>assume </b><a NAME="E1:4"/><i><font color="Green" title="E4">A1</font></i>: 
<font color="Maroon" title="c2">V1</font> is <a href="rlsub_1.html#V1" title="RLSUB_1:attr.1">linearly-closed</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c3">v</font>, <font color="Maroon" title="c4">u</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="E2:4"/><i><font color="Green" title="E5">A2</font></i>: 
<font color="Maroon" title="c3">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">V1</font>
 <b>and </b><br/><a NAME="E3:4"/><i><font color="Green" title="E6">A3</font></i>: 
<font color="Maroon" title="c4">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">V1</font>
 ;<br/>

<a NAME="E4:4"/>
( <font color="Maroon" title="c3">v</font> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c4">u</font></span>)</span> &amp;  <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c4">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">V1</font> )
 
<b>by </b><i><a class="txt" href="rlsub_1.html#E1:4"><i><font color="Green" title="E4">A1</font></i></a>, <a class="txt" href="rlsub_1.html#E3:4"><i><font color="Green" title="E6">A3</font></i></a>, <a class="ref" href="rlsub_1.html#T5" target="_self" title="RLSUB_1:th.5">Th5</a></i>;<br/>
<b>hence </b><a NAME="E5:4"/>
<font color="Maroon" title="c3">v</font> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c4">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">V1</font>
 <b>by </b><i><a class="txt" href="rlsub_1.html#E1:4"><i><font color="Green" title="E4">A1</font></i></a>, <a class="txt" href="rlsub_1.html#E2:4"><i><font color="Green" title="E5">A2</font></i></a>, <a class="ref" href="rlsub_1.html#D1" target="_self" title="RLSUB_1:def.1">Def1</a></i>;<br/>


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