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<b>let </b><font color="Maroon" title="c1">R</font> be   <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</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">W1</font>, <font color="Olive" title="b3">W2</font> being   <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <font color="Olive" title="b1">V</font> holds   <a href="rmod_2.html#K1" title="RMOD_2:func.1">(0).</a> <font color="Olive" title="b2">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rmod_2.html#K1" title="RMOD_2:func.1">(0).</a> <font color="Olive" title="b3">W2</font></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">W1</font>, <font color="Olive" title="b2">W2</font> being   <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <font color="Maroon" title="c2">V</font> holds   <a href="rmod_2.html#K1" title="RMOD_2:func.1">(0).</a> <font color="Olive" title="b1">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rmod_2.html#K1" title="RMOD_2:func.1">(0).</a> <font color="Olive" title="b2">W2</font></span><br/><b>let </b><font color="Maroon" title="c3">W1</font>, <font color="Maroon" title="c4">W2</font> be    <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</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_2.html#K1" title="RMOD_2:func.1">(0).</a> <font color="Maroon" title="c3">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rmod_2.html#K1" title="RMOD_2:func.1">(0).</a> <font color="Maroon" title="c4">W2</font></span><br/>







<a NAME="E1:40"/>
(  <a href="rmod_2.html#K1" title="RMOD_2:func.1">(0).</a> <font color="Maroon" title="c3">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rmod_2.html#K1" title="RMOD_2:func.1">(0).</a> <font color="Maroon" title="c2">V</font> &amp;  <a href="rmod_2.html#K1" title="RMOD_2:func.1">(0).</a> <font color="Maroon" title="c4">W2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rmod_2.html#K1" title="RMOD_2:func.1">(0).</a> <font color="Maroon" title="c2">V</font> )
 
<b>by </b><i><a class="ref" href="rmod_2.html#T47" target="_self" title="RMOD_2:th.47">Th47</a></i>;<br/>
<b>hence </b><a NAME="E2:40"/>
 <a href="rmod_2.html#K1" title="RMOD_2:func.1">(0).</a> <font color="Maroon" title="c3">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rmod_2.html#K1" title="RMOD_2:func.1">(0).</a> <font color="Maroon" title="c4">W2</font>
 ; <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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