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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E11">Th10</font></span>: <a NAME="T10"><span class="comment"><font color="firebrick">:: LMOD_7:10</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">K</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">K</font><br/>  for <font color="Olive" title="b3">a1</font>, <font color="Olive" title="b4">a2</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Olive" title="b2">V</font><br/>  for <font color="Olive" title="b5">W</font> being    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Olive" title="b2">V</font> holds <br/> ( <font color="Olive" title="b4">a2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">a1</font> <a href="vectsp_4.html#K3" title="VECTSP_4:func.3">+</a> <font color="Olive" title="b5">W</font> iff <font color="Olive" title="b3">a1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b4">a2</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b5">W</font> )</div></div>
