<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span>   defines <a href="rmod_4.html#V1" title="RMOD_4:attr.1">linearly-independent</a> <a onclick="hs(this)" href="javascript:()">RMOD_4:def 13 : <br/></a><span> 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#NM6" title="VECTSP_2:NM.6">RightMod</a> of <font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b3">IT</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b2">V</font> holds <br/> ( <font color="Olive" title="b3">IT</font> is  <a href="rmod_4.html#V1" title="RMOD_4:attr.1">linearly-independent</a>  iff  for <font color="Olive" title="b4">l</font> being    <a href="rmod_4.html#M2" title="RMOD_4:mode.2">Linear_Combination</a> of <font color="Olive" title="b3">IT</font>  st  <a href="rmod_4.html#K5" title="RMOD_4:func.5">Sum</a> <font color="Olive" title="b4">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b2">V</font> holds <br/> <a href="rmod_4.html#K2" title="RMOD_4:func.2">Carrier</a> <font color="Olive" title="b4">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  );<br/></span></div>
