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<div><span class="kw">theorem </span><a NAME="T16"><span class="comment"><font color="firebrick">:: LMOD_6:16</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">M1</font>, <font color="Olive" title="b3">M2</font>, <font color="Olive" title="b4">N</font> being   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">LeftMod</a> of <font color="Olive" title="b1">K</font>  st <font color="Olive" title="b2">M1</font> <a href="lmod_6.html#R1" title="LMOD_6:pred.1">c=</a> <font color="Olive" title="b4">N</font> &amp; <font color="Olive" title="b3">M2</font> <a href="lmod_6.html#R1" title="LMOD_6:pred.1">c=</a> <font color="Olive" title="b4">N</font> holds <br/>(  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b2">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b3">M2</font> &amp;  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b2">M1</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b3">M2</font> &amp; (  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">M1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b3">M2</font> implies <font color="Olive" title="b2">M1</font> <a href="lmod_6.html#R1" title="LMOD_6:pred.1">c=</a> <font color="Olive" title="b3">M2</font> ) &amp; ( (  for <font color="Olive" title="b5">n</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Olive" title="b4">N</font>  st <font color="Olive" title="b5">n</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b2">M1</font> holds <br/><font color="Olive" title="b5">n</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b3">M2</font> ) implies <font color="Olive" title="b2">M1</font> <a href="lmod_6.html#R1" title="LMOD_6:pred.1">c=</a> <font color="Olive" title="b3">M2</font> ) &amp; (  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b3">M2</font> &amp; <font color="Olive" title="b2">M1</font> is  <a href="vectsp_1.html#V7" title="VECTSP_1:attr.7">strict</a>  &amp; <font color="Olive" title="b3">M2</font> is  <a href="vectsp_1.html#V7" title="VECTSP_1:attr.7">strict</a>  implies <font color="Olive" title="b2">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">M2</font> ) &amp;  <a href="vectsp_4.html#K1" title="VECTSP_4:func.1">(0).</a> <font color="Olive" title="b2">M1</font> <a href="lmod_6.html#R1" title="LMOD_6:pred.1">c=</a> <font color="Olive" title="b3">M2</font> ) <span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_4.html#T12" onmouseover="rs('vectsp_4/T12')" onmouseout="rh()">VECTSP_4:12</a>, <a class="ref" href="vectsp_4.html#T18" onmouseover="rs('vectsp_4/T18')" onmouseout="rh()">VECTSP_4:18</a>, <a class="ref" href="vectsp_4.html#T27" onmouseover="rs('vectsp_4/T27')" onmouseout="rh()">VECTSP_4:27</a>, <a class="ref" href="vectsp_4.html#T28" onmouseover="rs('vectsp_4/T28')" onmouseout="rh()">VECTSP_4:28</a>, <a class="ref" href="vectsp_4.html#T29" onmouseover="rs('vectsp_4/T29')" onmouseout="rh()">VECTSP_4:29</a>, <a class="ref" href="vectsp_4.html#T40" onmouseover="rs('vectsp_4/T40')" onmouseout="rh()">VECTSP_4:40</a></span>;<br/></div></div>
