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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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">V</font> being  <a href="vectsp_2.html#NM7" title="VECTSP_2:NM.7">RightMod</a> of <font color="Maroon" title="c1">R</font><br/> for <font color="Olive" title="b2">A</font>, <font color="Olive" title="b3">B</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">V</font> holds   <a href="rmod_5.html#K1" title="RMOD_5:func.1">Lin</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b3">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="Olive" title="b2">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="Olive" title="b3">B</font></span>)</span></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">V</font> holds   <a href="rmod_5.html#K1" title="RMOD_5:func.1">Lin</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b2">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="Olive" title="b1">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="Olive" title="b2">B</font></span>)</span></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <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></span><br/>







<a NAME="E1:17"/>
(  <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  <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>, <a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></i>;<br/>
<b>hence </b><a NAME="E2:17"/>
 <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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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