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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E25">Def11</font></span>   defines <a href="aofa_a00.html#V3" title="AOFA_A00:attr.3">vf-free</a> <a onclick="hs(this)" href="javascript:()">AOFA_A00:def 11 : <br/></a><span> 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   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>  <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="aofa_a00.html#L1" title="AOFA_A00:struct.1">VarMSAlgebra</a> over <font color="Olive" title="b1">S</font> holds <br/> ( <font color="Olive" title="b3">A</font> is  <a href="aofa_a00.html#V3" title="AOFA_A00:attr.3">vf-free</a>  iff  for <font color="Olive" title="b4">s</font>, <font color="Olive" title="b5">r</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="b6">t</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> holds  <span class="p1">(<span class="default"><a href="aofa_a00.html#K10" title="AOFA_A00:func.10">vf</a> <font color="Olive" title="b6">t</font></span>)</span> <a href="msafree4.html#K1" title="MSAFREE4:func.1">.</a> <font color="Olive" title="b5">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b6">t</font> <a href="trees_2.html#K5" title="TREES_2:func.5">|</a> <font color="Olive" title="b7">p</font></span>)</span> where <font color="Olive" title="b7">p</font> is    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b6">t</font> : <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b6">t</font> <a href="trees_2.html#K5" title="TREES_2:func.5">|</a> <font color="Olive" title="b7">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span>)</span> <a href="xtuple_0.html#K2" title="XTUPLE_0:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">r</font> </span> } </span>  );<br/></span></div>
