<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">V</font> be  non <a href="struct_0.html#V3">empty</a> <a href="rlvect_1.html#V3">Abelian</a> <a href="rlvect_1.html#V4">add-associative</a> <a href="rlvect_1.html#V5">right_zeroed</a>  <a href="rlvect_1.html#L1">LoopStr</a> ;<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>, <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>assume </b><a NAME="E1:16"/><i><font color="Green">E46</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="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E3:16"/><i><font color="Green">E52</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="E4:16"/><i><font color="Green">E53</font></i>: 
( <font color="Maroon">F</font> is <a href="funct_1.html#V2">one-to-one</a> &amp;  <a href="rlvect_2.html#K2" 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="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E6:16"/><i><font color="Green">E54</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="E7:16"/><i><font color="Green">E55</font></i>: 
 <a href="rlvect_2.html#K2" 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="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E9:16"/><i><font color="Green">E56</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="E10:16"/><i><font color="Green">E57</font></i>: 
 <a href="rlvect_2.html#K2" 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="E11:16"/><i><font color="Green">E60</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="E12:16"/>
<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="rlvect_2.html#K2" 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="rlvect_2.html#K2" 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="rlvect_2.html#K2" 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/>


</div>
