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

<b>let </b><font color="Maroon" title="c5">S</font>, <font color="Maroon" title="c6">T</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">V</font> <a href="lmod_7.html#K7" title="LMOD_7:func.7">..</a> <font color="Maroon" title="c3">W</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:42_1_2"/><i><font color="Green" title="E15">A3</font></i>: 
for <font color="Olive" title="b1">a</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</font>  st <font color="Maroon" title="c4">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="lmod_7.html#K8" title="LMOD_7:func.8">..</a> <font color="Maroon" title="c3">W</font> holds <br/><font color="Maroon" title="c5">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="lmod_7.html#K8" title="LMOD_7:func.8">..</a> <font color="Maroon" title="c3">W</font>
 <b>and </b><br/><a NAME="E2:42_1_2"/><i><font color="Green" title="E16">A4</font></i>: 
for <font color="Olive" title="b1">a</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</font>  st <font color="Maroon" title="c4">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="lmod_7.html#K8" title="LMOD_7:func.8">..</a> <font color="Maroon" title="c3">W</font> holds <br/><font color="Maroon" title="c6">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="lmod_7.html#K8" title="LMOD_7:func.8">..</a> <font color="Maroon" title="c3">W</font>
 ;<br/>

<b>consider </b><font color="Maroon" title="c7">a1</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</font><b> such that </b><br/><a NAME="E4:42_1_2"/><i><font color="Green" title="E17">A5</font></i>: 
<font color="Maroon" title="c4">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">a1</font> <a href="lmod_7.html#K8" title="LMOD_7:func.8">..</a> <font color="Maroon" title="c3">W</font>
 <b>by </b><i><a class="ref" href="lmod_7.html#T19" target="_self" title="LMOD_7:th.19">Th19</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c5">S</font> = 
<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c7">a1</font></span>)</span> <a href="lmod_7.html#K8" title="LMOD_7:func.8">..</a> <font color="Maroon" title="c3">W</font>
<b>by </b><i><a class="txt" href="lmod_7.html#E1:42_1_2"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="lmod_7.html#E4:42_1_2"><i><font color="Green" title="E17">A5</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c6">T</font>
<b>by </b><i><a class="txt" href="lmod_7.html#E2:42_1_2"><i><font color="Green" title="E16">A4</font></i></a>, <a class="txt" href="lmod_7.html#E4:42_1_2"><i><font color="Green" title="E17">A5</font></i></a></i>
;<br/>


</div>
