<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E27">Th27</font></span>: <a NAME="T27"><span class="comment"><font color="firebrick">:: MSAFREE4:27</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   non  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>   <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> <br/>  for <font color="Olive" title="b2">A1</font>, <font color="Olive" title="b3">A2</font> being    <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> over <font color="Olive" title="b1">S</font>  st  <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(#  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b2">A1</font>, the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Olive" title="b2">A1</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(#  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b3">A2</font>, the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Olive" title="b3">A2</font> #) holds <br/> for <font color="Olive" title="b4">B1</font> being   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <font color="Olive" title="b2">A1</font><br/>  for <font color="Olive" title="b5">B2</font> being   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <font color="Olive" title="b3">A2</font>  st <font color="Olive" title="b4">B1</font> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a> <font color="Olive" title="b5">B2</font> &amp; <font color="Olive" title="b4">B1</font> is  <a href="msualg_2.html#V3" title="MSUALG_2:attr.3">opers_closed</a>  holds <br/><font color="Olive" title="b5">B2</font> is  <a href="msualg_2.html#V3" title="MSUALG_2:attr.3">opers_closed</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="msafree4.html#T24" target="_self" onmouseover="rs('msafree4/T24')" onmouseout="rh()">Th24</a></span>;<br/></div></div>
