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<b>let </b><font color="Maroon" title="c1">K</font> be   <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>;<br/><b>let </b><font color="Maroon" title="c2">M</font>, <font color="Maroon" title="c3">N</font> be   <a href="vectsp_2.html#NM6" title="VECTSP_2:NM.6">LeftMod</a> of <font color="Maroon" title="c1">K</font>;<br/>





<b>assume </b><a NAME="E1:27"/>
<font color="Maroon" title="c2">M</font> <a href="lmod_6.html#R1" title="LMOD_6:pred.1">c=</a> <font color="Maroon" title="c3">N</font>
 ;<br/>

<a NAME="E2:27"/><b>then </b><i><font color="Green" title="E11">A1</font></i>: 
<font color="Maroon" title="c2">M</font> is    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c3">N</font>
 
<b>by </b><i><a class="ref" href="lmod_6.html#D7" target="_self" title="LMOD_6:def.7">Def7</a></i>;<br/>
<a NAME="E3:27"/>
<font color="Maroon" title="c3">N</font> is    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of  <a href="vectsp_4.html#K2" title="VECTSP_4:func.2">(Omega).</a> <font color="Maroon" title="c3">N</font>
 
<b>by </b><i><a class="ref" href="lmod_6.html#T4" target="_self" title="LMOD_6:th.4">Th4</a></i>;<br/>
<a NAME="E4:27"/><b>then </b>
<font color="Maroon" title="c2">M</font> is    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of  <a href="vectsp_4.html#K2" title="VECTSP_4:func.2">(Omega).</a> <font color="Maroon" title="c3">N</font>
 
<b>by </b><i><a class="txt" href="lmod_6.html#E2:27"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="vectsp_4.html#T34" title="VECTSP_4:th.34">VECTSP_4:34</a></i>;<br/>
<b>hence </b><a NAME="E5:27"/>
<font color="Maroon" title="c2">M</font> <a href="lmod_6.html#R1" title="LMOD_6:pred.1">c=</a>  <a href="vectsp_4.html#K2" title="VECTSP_4:func.2">(Omega).</a> <font color="Maroon" title="c3">N</font>
 <b>by </b><i><a class="ref" href="lmod_6.html#D7" target="_self" title="LMOD_6:def.7">Def7</a></i>;<br/>


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