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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E48">Th137</font></span>: <a NAME="T137"><span class="comment"><font color="firebrick">:: ZMODUL01:137</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><br/>  for <font color="Olive" title="b5">v</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Olive" title="b2">V</font>  st <font color="Olive" title="b2">V</font> <a href="vectsp_5.html#R1" title="VECTSP_5:pred.1">is_the_direct_sum_of</a> <font color="Olive" title="b3">W1</font>,<font color="Olive" title="b4">W2</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b5">v</font> <a href="vectsp_5.html#K4" title="VECTSP_5:func.4">|--</a> (<font color="Olive" title="b3">W1</font>,<font color="Olive" title="b4">W2</font>)</span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">v</font> <a href="vectsp_5.html#K4" title="VECTSP_5:func.4">|--</a> (<font color="Olive" title="b4">W2</font>,<font color="Olive" title="b3">W1</font>)</span>)</span> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_5.html#T51" onmouseover="rs('vectsp_5/T51')" onmouseout="rh()">VECTSP_5:51</a></span>;<br/></div></div>
