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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E40">Th57</font></span>: <a NAME="T57"><span class="comment"><font color="firebrick">:: RMOD_2:57</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#NM6" title="VECTSP_2:NM.6">RightMod</a> of <font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b3">u</font>, <font color="Olive" title="b4">v</font> being   <a href="vectsp_2.html#NM4" title="VECTSP_2:NM.4">Vector</a> of <font color="Olive" title="b2">V</font><br/>  for <font color="Olive" title="b5">W</font> being    <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <font color="Olive" title="b2">V</font> holds <br/> ( <font color="Olive" title="b3">u</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b4">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">v</font> <a href="rmod_2.html#K3" title="RMOD_2:func.3">+</a> <font color="Olive" title="b5">W</font> iff <font color="Olive" title="b3">u</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b5">W</font> )</div></div>
