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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">T</font> be  <a href="finset_1.html#V1">finite</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">S</font> be  <a href="finset_1.html#V1">finite</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">V</font>;<br/>







<b>set </b><font color="Maroon">A</font> = <font color="Maroon">S</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">T</font>;<br/>
<b>set </b><font color="Maroon">B</font> = <font color="Maroon">T</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">S</font>;<br/>
<b>set </b><font color="Maroon">Z</font> = <span class="p1">(<span class="default"><font color="Maroon">S</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">T</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">S</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">I</font> = <font color="Maroon">T</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">S</font>;<br/>
<a NAME="E1:13"/>
<span class="p1">(<span class="default"><font color="Maroon">S</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">T</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">S</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font> <a href="subset_1.html#K5">\+\</a> <font color="Maroon">S</font>
 
;<br/>
<a NAME="E2:13"/><b>then </b><i><font color="Green">E48</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">S</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">T</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">S</font></span>)</span> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">T</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">S</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">S</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">T</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><font color="Maroon">T</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">S</font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">S</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">S</font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T93">XBOOLE_1:93</a>, <a class="ref" href="xboole_1.html#T103">XBOOLE_1:103</a></i>;<br/>
<a NAME="E3:13"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">S</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">T</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">T</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">S</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T82">XBOOLE_1:82</a></i>;<br/>
<a NAME="E4:13"/><i><font color="Green">E50</font></i>: 
( <font color="Maroon">S</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">T</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">T</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">S</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">S</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">T</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">S</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">S</font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T51">XBOOLE_1:51</a>, <a class="ref" href="xboole_1.html#T89">XBOOLE_1:89</a></i>;<br/>
<a NAME="E5:13"/><i><font color="Green">E52</font></i>: 
( <font color="Maroon">T</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">S</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">T</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">S</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">S</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">S</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T51">XBOOLE_1:51</a>, <a class="ref" href="xboole_1.html#T89">XBOOLE_1:89</a></i>;<br/>
<span class="p1">(<span class="default"><a href="rmod_4.html#K1" target="_self">Sum</a> <span class="p2">(<span class="default"><font color="Maroon">T</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">S</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rmod_4.html#K1" target="_self">Sum</a> <span class="p2">(<span class="default"><font color="Maroon">T</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">S</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rmod_4.html#K1" target="_self">Sum</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">S</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">T</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p4">(<span class="default"><font color="Maroon">T</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">S</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rmod_4.html#K1" target="_self">Sum</a> <span class="p3">(<span class="default"><font color="Maroon">T</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">S</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rmod_4.html#K1" target="_self">Sum</a> <span class="p2">(<span class="default"><font color="Maroon">T</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">S</font></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rmod_4.html#K1" target="_self">Sum</a> <span class="p4">(<span class="default"><font color="Maroon">S</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><a href="rmod_4.html#K1" target="_self">Sum</a> <span class="p4">(<span class="default"><font color="Maroon">T</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">S</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rmod_4.html#K1" target="_self">Sum</a> <span class="p3">(<span class="default"><font color="Maroon">T</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">S</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rmod_4.html#K1" target="_self">Sum</a> <span class="p2">(<span class="default"><font color="Maroon">T</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">S</font></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rmod_4.html#K1" target="_self">Sum</a> <span class="p3">(<span class="default"><font color="Maroon">S</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rmod_4.html#K1" target="_self">Sum</a> <span class="p4">(<span class="default"><font color="Maroon">T</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">S</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><a href="rmod_4.html#K1" target="_self">Sum</a> <span class="p4">(<span class="default"><font color="Maroon">T</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">S</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rmod_4.html#K1" target="_self">Sum</a> <span class="p2">(<span class="default"><font color="Maroon">T</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">S</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D6">RLVECT_1:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rmod_4.html#K1" target="_self">Sum</a> <span class="p3">(<span class="default"><font color="Maroon">S</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rmod_4.html#K1" target="_self">Sum</a> <span class="p3">(<span class="default"><font color="Maroon">T</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">S</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rmod_4.html#K1" target="_self">Sum</a> <span class="p3">(<span class="default"><font color="Maroon">T</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">S</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rmod_4.html#K1" target="_self">Sum</a> <span class="p3">(<span class="default"><font color="Maroon">T</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">S</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D6">RLVECT_1:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rmod_4.html#K1" target="_self">Sum</a> <font color="Maroon">S</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rmod_4.html#K1" target="_self">Sum</a> <span class="p3">(<span class="default"><font color="Maroon">T</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">S</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rmod_4.html#K1" target="_self">Sum</a> <span class="p3">(<span class="default"><font color="Maroon">T</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">S</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rmod_4.html#K1" target="_self">Sum</a> <font color="Maroon">T</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rmod_4.html#K1" target="_self">Sum</a> <font color="Maroon">S</font></span>)</span>
<b>by </b><i>, </i>
;<br/>
<b>hence </b><a NAME="E7:13"/>
 <a href="rmod_4.html#K1" target="_self">Sum</a> <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">S</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rmod_4.html#K1" target="_self">Sum</a> <font color="Maroon">T</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rmod_4.html#K1" target="_self">Sum</a> <font color="Maroon">S</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><a href="rmod_4.html#K1" target="_self">Sum</a> <span class="p2">(<span class="default"><font color="Maroon">T</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">S</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="rlsub_2.html#T78">RLSUB_2:78</a></i>;<br/>


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