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<div><span class="kw">theorem </span><a NAME="T22"><span class="comment"><font color="firebrick">:: ZMODUL04:22</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font> being   <a href="zmodul01.html#NM1" title="ZMODUL01:NM.1">Z_Module</a><br/>  for <font color="Olive" title="b2">W1</font>, <font color="Olive" title="b3">W2</font> being   <a href="zmodul01.html#NM3" title="ZMODUL01:NM.3">Submodule</a> of <font color="Olive" title="b1">V</font><br/>  for <font color="Olive" title="b4">W1s</font>, <font color="Olive" title="b5">W2s</font> being   <a href="vectsp_1.html#V7" title="VECTSP_1:attr.7">strict</a>  <a href="zmodul01.html#NM3" title="ZMODUL01:NM.3">Submodule</a> of <font color="Olive" title="b1">V</font>  st <font color="Olive" title="b4">W1s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_4.html#K2" title="VECTSP_4:func.2">(Omega).</a> <font color="Olive" title="b2">W1</font> &amp; <font color="Olive" title="b5">W2s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_4.html#K2" title="VECTSP_4:func.2">(Omega).</a> <font color="Olive" title="b3">W2</font> holds <br/><font color="Olive" title="b4">W1s</font> <a href="zmodul01.html#K1" title="ZMODUL01:func.1">+</a> <font color="Olive" title="b5">W2s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">W1</font> <a href="zmodul01.html#K1" title="ZMODUL01:func.1">+</a> <font color="Olive" title="b3">W2</font></div></div>
