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<div><span class="kw">theorem </span><a NAME="T121"><span class="comment"><font color="firebrick">:: ZMODUL01:121</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">W1</font>, <font color="Olive" title="b4">W2</font> being   <a href="zmodul01.html#NM3" title="ZMODUL01:NM.3">Submodule</a> of <font color="Olive" title="b2">V</font> holds <br/> ( ( <font color="Olive" title="b3">W1</font> is   <a href="zmodul01.html#NM3" title="ZMODUL01:NM.3">Submodule</a> of <font color="Olive" title="b4">W2</font> or <font color="Olive" title="b4">W2</font> is   <a href="zmodul01.html#NM3" title="ZMODUL01:NM.3">Submodule</a> of <font color="Olive" title="b3">W1</font> ) iff  ex <font color="Olive" title="b5">W</font> being   <a href="zmodul01.html#NM3" title="ZMODUL01:NM.3">Submodule</a> of <font color="Olive" title="b2">V</font> st  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b5">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b3">W1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b4">W2</font> ) <span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_5.html#T35" onmouseover="rs('vectsp_5/T35')" onmouseout="rh()">VECTSP_5:35</a></span>;<br/></div></div>
