<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E65">Th23</font></span>: <a NAME="T82"><span class="comment"><font color="firebrick">:: MSAFREE5:82</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">s</font> being   <a href="msualg_1.html#NM1" title="MSUALG_1:NM.1">SortSymbol</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">X</font> being  <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a> <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b4">x</font> being    <a href="msafree4.html#M1" title="MSAFREE4:mode.1">Element</a> of <font color="Olive" title="b3">X</font> <a href="msafree4.html#K1" title="MSAFREE4:func.1">.</a> <font color="Olive" title="b2">s</font><br/>  for <font color="Olive" title="b5">t</font>, <font color="Olive" title="b6">t1</font> being   <a href="msafree3.html#NM1" title="MSAFREE3:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="msafree3.html#K1" title="MSAFREE3:func.1">Free</a> (<font color="Olive" title="b1">S</font>,<font color="Olive" title="b3">X</font>)</span>)</span>  st <font color="Olive" title="b5">t</font> is <font color="Olive" title="b4">x</font> <a href="msafree5.html#V9" title="MSAFREE5:attr.9">-omitting</a>  holds <br/>(<font color="Olive" title="b5">t</font>,<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b4">x</font>,<font color="Olive" title="b2">s</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>) <a href="trees_4.html#K9" title="TREES_4:func.9">&lt;-</a> <font color="Olive" title="b6">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">t</font></div></div>
