<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E5">RL5Def4</font></span>   defines <a href="zmodul05.html#K1" title="ZMODUL05:func.1">Submodules_of</a> <a onclick="hs(this)" href="javascript:()">ZMODUL05:def 1 : <br/></a><span> for <font color="Olive" title="b1">V</font> being   <a href="vectsp_7.html#V3" title="VECTSP_7:attr.3">free</a>   <a href="zmodul03.html#V1" title="ZMODUL03:attr.1">finite-rank</a>  <a href="zmodul01.html#NM1" title="ZMODUL01:NM.1">Z_Module</a><br/>  for <font color="Olive" title="b2">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive">b<sub>3</sub></font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds <br/> ( <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">n</font> <a href="zmodul05.html#K1" title="ZMODUL05:func.1">Submodules_of</a> <font color="Olive" title="b1">V</font> iff  for <font color="Olive" title="b4">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  holds <br/> ( <font color="Olive" title="b4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive">b<sub>3</sub></font> iff  ex <font color="Olive" title="b5">W</font> being   <a href="vectsp_1.html#V7" title="VECTSP_1:attr.7">strict</a>   <a href="vectsp_7.html#V3" title="VECTSP_7:attr.3">free</a>  <a href="zmodul01.html#NM3" title="ZMODUL01:NM.3">Submodule</a> of <font color="Olive" title="b1">V</font> st <br/>( <font color="Olive" title="b5">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">x</font> &amp;  <a href="zmodul03.html#K1" title="ZMODUL03:func.1">rank</a> <font color="Olive" title="b5">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">n</font> ) ) );<br/></span></div>
