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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E7">Th14</font></span>: <a NAME="T14"><span class="comment"><font color="firebrick">:: LMOD_6:14</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">M</font>, <font color="Olive" title="b3">N</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="b4">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b2">M</font> <a href="lmod_6.html#R1" title="LMOD_6:pred.1">c=</a> <font color="Olive" title="b3">N</font> holds <br/>( ( <font color="Olive" title="b4">x</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b2">M</font> implies <font color="Olive" title="b4">x</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b3">N</font> ) &amp; ( <font color="Olive" title="b4">x</font> is   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Olive" title="b2">M</font> implies <font color="Olive" title="b4">x</font> is   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Olive" title="b3">N</font> ) ) <span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_4.html#T9" onmouseover="rs('vectsp_4/T9')" onmouseout="rh()">VECTSP_4:9</a>, <a class="ref" href="vectsp_4.html#T10" onmouseover="rs('vectsp_4/T10')" onmouseout="rh()">VECTSP_4:10</a></span>;<br/></div></div>
