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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>assume </b><a NAME="E1:12"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">T</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">S</font>
 ;<br/>

<b>consider </b><font color="Maroon">F</font> being   <a href="struct_0.html#NM7">FinSequence</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E3:12"/><i><font color="Green">E49</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">S</font>
 <b>and </b><br/><a NAME="E4:12"/><i><font color="Green">E50</font></i>: 
( <font color="Maroon">F</font> is <a href="funct_1.html#V2">one-to-one</a> &amp;  <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>  <a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">F</font> )
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">G</font> being   <a href="struct_0.html#NM7">FinSequence</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E6:12"/><i><font color="Green">E52</font></i>: 
(  <a href="relat_1.html#K2">rng</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font> &amp; <font color="Maroon">G</font> is <a href="funct_1.html#V2">one-to-one</a> )
 <b>and </b><br/><a NAME="E7:12"/><i><font color="Green">E53</font></i>: 
 <a href="rmod_4.html#K1" target="_self">Sum</a> <font color="Maroon">T</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">G</font>
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">H</font> being   <a href="struct_0.html#NM7">FinSequence</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E9:12"/><i><font color="Green">E54</font></i>: 
(  <a href="relat_1.html#K2">rng</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">S</font> &amp; <font color="Maroon">H</font> is <a href="funct_1.html#V2">one-to-one</a> )
 <b>and </b><br/><a NAME="E10:12"/><i><font color="Green">E55</font></i>: 
 <a href="rmod_4.html#K1" target="_self">Sum</a> <font color="Maroon">S</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">H</font>
 <b>by </b><i/>;<br/>
<b>set </b><font color="Maroon">I</font> = <font color="Maroon">G</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">H</font>;<br/>
<a NAME="E11:12"/><i><font color="Green">E56</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">H</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">F</font>
 
<b>by </b><i>, , , <a class="ref" href="finseq_1.html#T44">FINSEQ_1:44</a></i>;<br/>
<a NAME="E12:12"/>
<font color="Maroon">G</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">H</font> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i>, , , <a class="ref" href="finseq_3.html#T98">FINSEQ_3:98</a></i>;<br/>
<b>hence </b> <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="rlvect_1.html#K9">Sum</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">H</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="rlvect_1.html#T59">RLVECT_1:59</a></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>, , <a class="ref" href="rlvect_1.html#T58">RLVECT_1:58</a></i>
;<br/><br/>


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