<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E28">Th45</font></span>: <a NAME="T45"><span class="comment"><font color="firebrick">:: MATHMORP:45</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">T</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>   <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a>   <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>   <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>   <a href="rlvect_1.html#L1" title="RLVECT_1:struct.1">RLSStruct</a> <br/>  for <font color="Olive" title="b2">X</font>, <font color="Olive" title="b3">Y</font>, <font color="Olive" title="b4">B</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">T</font>  st <font color="Olive" title="b2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">Y</font> holds <br/>( <font color="Olive" title="b2">X</font> <a href="mathmorp.html#K4" title="MATHMORP:func.4">(O)</a> <font color="Olive" title="b4">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">Y</font> <a href="mathmorp.html#K4" title="MATHMORP:func.4">(O)</a> <font color="Olive" title="b4">B</font> &amp; <font color="Olive" title="b2">X</font> <a href="mathmorp.html#K5" title="MATHMORP:func.5">(o)</a> <font color="Olive" title="b4">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">Y</font> <a href="mathmorp.html#K5" title="MATHMORP:func.5">(o)</a> <font color="Olive" title="b4">B</font> )</div></div>
