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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/>





<i><font color="Green">E30</font></i>: the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rmod_2.html#K1">(0).</a> <font color="Maroon">V</font></span>)</span> <a href="rmod_3.html#K2" target="_self">/\</a> <font color="Maroon">W</font></span>)</span> = 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="rmod_2.html#K1">(0).</a> <font color="Maroon">V</font></span>)</span> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W</font>
<b>by </b><i/>
<br/>.= 
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K8">/\</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#D3">RMOD_2:def 3</a></i>
;<br/>
<a NAME="E2:25"/>
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W</font>
 
<b>by </b><i><a class="ref" href="rmod_2.html#T25">RMOD_2:25</a></i>;<br/>
<a NAME="E3:25"/><b>then </b>
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W</font>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>
<a NAME="E4:25"/><b>then </b>
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <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="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/>
<a NAME="E5:25"/><b>then </b>
( <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font></span>)</span></span><a href="domain_1.html#K6">}</a></span> &amp; the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="rmod_2.html#K1">(0).</a> <font color="Maroon">V</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font></span>)</span></span><a href="domain_1.html#K6">}</a></span> )
 
<b>by </b><i><a class="ref" href="rmod_2.html#D3">RMOD_2:def 3</a>, <a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>;<br/>
<b>hence </b><a NAME="E6:25"/>
<span class="p1">(<span class="default"><a href="rmod_2.html#K1">(0).</a> <font color="Maroon">V</font></span>)</span> <a href="rmod_3.html#K2" target="_self">/\</a> <font color="Maroon">W</font> <a href="hidden.html#R1">=</a>  <a href="rmod_2.html#K1">(0).</a> <font color="Maroon">V</font>
 <b>by </b><i>, <a class="ref" href="rmod_2.html#T37">RMOD_2:37</a></i>;<br/>

<b>hence </b><a NAME="E7:25"/>
<font color="Maroon">W</font> <a href="rmod_3.html#K2" target="_self">/\</a> <span class="p1">(<span class="default"><a href="rmod_2.html#K1">(0).</a> <font color="Maroon">V</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rmod_2.html#K1">(0).</a> <font color="Maroon">V</font>
 <b>by </b><i/>;<br/>


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