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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>thus </b><a NAME="E1:14"/>
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 <span class="p1">(<span class="default"><a href="rmod_2.html#K2">(Omega).</a> <font color="Maroon">V</font></span>)</span>
 <b>by </b><i><a class="ref" href="rmod_2.html#D2">RMOD_2:def 2</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="rmod_2.html#D2">RMOD_2:def 2</a><br/>

<b>thus </b><a NAME="E2:14"/>
( the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">W</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U2">Zero</a> of <span class="p1">(<span class="default"><a href="rmod_2.html#K2">(Omega).</a> <font color="Maroon">V</font></span>)</span> &amp; the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">W</font> <a href="hidden.html#R1">=</a> the <a href="rlvect_1.html#U1">add</a> of <span class="p1">(<span class="default"><a href="rmod_2.html#K2">(Omega).</a> <font color="Maroon">V</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W</font></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; the <a href="vectsp_2.html#U1">rmult</a> of <font color="Maroon">W</font> <a href="hidden.html#R1">=</a> the <a href="vectsp_2.html#U1">rmult</a> of <span class="p1">(<span class="default"><a href="rmod_2.html#K2">(Omega).</a> <font color="Maroon">V</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 <b>by </b><i><a class="ref" href="rmod_2.html#D2">RMOD_2:def 2</a></i>;<br/>


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