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<b>let </b><font color="Maroon" title="c1">R</font> be   <a href="vectsp_2.html#NM2" title="VECTSP_2:NM.2">domRing</a>;<br/><b>let </b><font color="Maroon" title="c2">V</font> be   <a href="vectsp_2.html#NM7" title="VECTSP_2:NM.7">RightMod</a> of <font color="Maroon" title="c1">R</font>;<br/><b>let </b><font color="Maroon" title="c3">A</font>, <font color="Maroon" title="c4">B</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">V</font>;<br/>







<a NAME="E1:17"/>
( <font color="Maroon" title="c3">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">A</font> &amp; <font color="Maroon" title="c3">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">B</font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E2:17"/><b>then </b>
(  <a href="rmod_5.html#K1" title="RMOD_5:func.1">Lin</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">B</font></span>)</span> is    <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of  <a href="rmod_5.html#K1" title="RMOD_5:func.1">Lin</a> <font color="Maroon" title="c3">A</font> &amp;  <a href="rmod_5.html#K1" title="RMOD_5:func.1">Lin</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">B</font></span>)</span> is    <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of  <a href="rmod_5.html#K1" title="RMOD_5:func.1">Lin</a> <font color="Maroon" title="c4">B</font> )
 
<b>by </b><i><a class="ref" href="rmod_5.html#T15" target="_self" title="RMOD_5:th.15">Th15</a></i>;<br/>
<b>hence </b><a NAME="E3:17"/>
 <a href="rmod_5.html#K1" title="RMOD_5:func.1">Lin</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">B</font></span>)</span> is    <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <span class="p1">(<span class="default"><a href="rmod_5.html#K1" title="RMOD_5:func.1">Lin</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="rmod_3.html#K2" title="RMOD_3:func.2">/\</a> <span class="p1">(<span class="default"><a href="rmod_5.html#K1" title="RMOD_5:func.1">Lin</a> <font color="Maroon" title="c4">B</font></span>)</span>
 <b>by </b><i><a class="ref" href="rmod_3.html#T24" title="RMOD_3:th.24">RMOD_3:24</a></i>;<br/>


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