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<b>let </b><font color="Maroon">R</font> be   <a href="funcsdom.html#NM1">Ring</a>;<br/><b>let </b><font color="Maroon">V</font> be   <a href="vectsp_2.html#NM7">RightMod</a> of <font color="Maroon">R</font>;<br/><b>let </b><font color="Maroon">W</font> be    <a href="rmod_2.html#M1">Submodule</a> of <font color="Maroon">V</font>;<br/>





<b>consider </b><font color="Maroon">W'</font> being  <a href="vectsp_2.html#V3">strict</a>  <a href="rmod_2.html#M1">Submodule</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E2:15"/><i><font color="Green">E30</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W'</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="rmod_2.html#K2">(Omega).</a> <font color="Maroon">V</font></span>)</span>
 ;<br/>
<a NAME="E3:15"/><i><font color="Green">E33</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W'</font>
 
<b>by </b><i>, <a class="ref" href="rmod_2.html#D2">RMOD_2:def 2</a></i>;<br/>
<a NAME="E4:15"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">W'</font> is    <a href="rmod_2.html#M1">Submodule</a> of  <a href="rmod_2.html#K2">(Omega).</a> <font color="Maroon">V</font>
 
<b>by </b><i/>;<br/>
<font color="Maroon">W</font> <a href="rmod_3.html#K1" target="_self">+</a> <span class="p1">(<span class="default"><a href="rmod_2.html#K2">(Omega).</a> <font color="Maroon">V</font></span>)</span> = 
<font color="Maroon">W</font> <a href="rmod_3.html#K1" target="_self">+</a> <font color="Maroon">W'</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">W'</font>
<b>by </b><i>, </i>
<br/>.= 
 <a href="vectsp_2.html#G1">RightModStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font>,the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">V</font>,the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">V</font>,the <a href="vectsp_2.html#U1">rmult</a> of <font color="Maroon">V</font> #)
<b>by </b><i>, , <a class="ref" href="rmod_2.html#T39">RMOD_2:39</a></i>
;<br/>
<b>hence </b><a NAME="E6:15"/>
( <span class="p1">(<span class="default"><a href="rmod_2.html#K2">(Omega).</a> <font color="Maroon">V</font></span>)</span> <a href="rmod_3.html#K1" target="_self">+</a> <font color="Maroon">W</font> <a href="hidden.html#R1">=</a>  <a href="vectsp_2.html#G1">RightModStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font>,the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">V</font>,the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">V</font>,the <a href="vectsp_2.html#U1">rmult</a> of <font color="Maroon">V</font> #) &amp; <font color="Maroon">W</font> <a href="rmod_3.html#K1" target="_self">+</a> <span class="p1">(<span class="default"><a href="rmod_2.html#K2">(Omega).</a> <font color="Maroon">V</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="vectsp_2.html#G1">RightModStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font>,the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">V</font>,the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">V</font>,the <a href="vectsp_2.html#U1">rmult</a> of <font color="Maroon">V</font> #) )
 <b>by </b><i/>;<br/>


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