<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T18"><span class="comment"><font color="firebrick">:: ZMODUL02:18</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</font> being   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive" title="b2">V</font> being   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">LeftMod</a> of <font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b3">A</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b2">V</font>  st  not <font color="Olive" title="b1">R</font> is  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>  holds <br/>( ( <font color="Olive" title="b3">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b3">A</font> is  <a href="vectsp_4.html#V1" title="VECTSP_4:attr.1">linearly-closed</a>  ) iff  for <font color="Olive" title="b4">l</font> being    <a href="vectsp_6.html#M2" title="VECTSP_6:mode.2">Linear_Combination</a> of <font color="Olive" title="b3">A</font> holds   <a href="vectsp_6.html#K4" title="VECTSP_6:func.4">Sum</a> <font color="Olive" title="b4">l</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">A</font> ) <span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_6.html#T14" onmouseover="rs('vectsp_6/T14')" onmouseout="rh()">VECTSP_6:14</a></span>;<br/></div></div>
