<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T41"><span class="comment"><font color="firebrick">:: AOFA_A00:41</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">X</font> being  <a href="relat_1.html#V2" title="RELAT_1:attr.2">V2</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="b3">A</font> being  <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="msafree4.html#V5" title="MSAFREE4:attr.5">-terms</a>   <a href="msafree4.html#V6" title="MSAFREE4:attr.6">all_vars_including</a>   <a href="aofa_a00.html#V3" title="AOFA_A00:attr.3">vf-free</a>   <a href="aofa_a00.html#L1" title="AOFA_A00:struct.1">VarMSAlgebra</a> over <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b4">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="b5">x</font> being   <a href="msualg_6.html#NM1" title="MSUALG_6:NM.1">Element</a> of <font color="Olive" title="b3">A</font>,<font color="Olive" title="b4">s</font>  st <font color="Olive" title="b5">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="msafree.html#K13" title="MSAFREE:func.13">FreeGen</a> <font color="Olive" title="b2">X</font></span>)</span> <a href="msafree4.html#K1" title="MSAFREE4:func.1">.</a> <font color="Olive" title="b4">s</font> holds <br/> <a href="aofa_a00.html#K10" title="AOFA_A00:func.10">vf</a> <font color="Olive" title="b5">x</font> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a> <font color="Olive" title="b4">s</font> <a href="aofa_a00.html#K2" title="AOFA_A00:func.2">-singleton</a> <font color="Olive" title="b5">x</font></div></div>
