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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E61">Th68</font></span>: <a NAME="T68"><span class="comment"><font color="firebrick">:: AOFA_A01:68</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="aofa_a00.html#V16" title="AOFA_A00:attr.16">bool-correct</a>  4,1 <a href="aofa_a00.html#V18" title="AOFA_A00:attr.18">integer</a>   <a href="aofa_a00.html#L6" title="AOFA_A00:struct.6">BoolSignature</a> <br/>  for <font color="Olive" title="b2">X</font> being  <a href="relat_1.html#V2" title="RELAT_1:attr.2">V3</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">T</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="msafree4.html#V7" title="MSAFREE4:attr.7">inheriting_operations</a>   <a href="msafree4.html#V8" title="MSAFREE4:attr.8">free_in_itself</a>   <a href="aofa_a00.html#V3" title="AOFA_A00:attr.3">vf-free</a>   <a href="aofa_a01.html#V1" title="AOFA_A01:attr.1">integer</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">G</font> being   <a href="aofa_a01.html#V4" title="AOFA_A01:attr.4">basic</a>   <a href="aofa_a00.html#L4" title="AOFA_A00:struct.4">GeneratorSystem</a> over <font color="Olive" title="b1">S</font>,<font color="Olive" title="b2">X</font>,<font color="Olive" title="b3">T</font><br/>  for <font color="Olive" title="b5">A</font> being   <a href="aofa_a00.html#NM5" title="AOFA_A00:NM.5">IfWhileAlgebra</a> of  the <a href="aofa_a00.html#U4" title="AOFA_A00:sel.4">generators</a> of <font color="Olive" title="b4">G</font>  st <font color="Olive" title="b5">A</font> is  <a href="aofa_a01.html#V5" title="AOFA_A01:attr.5">elementary</a>  holds <br/> for <font color="Olive" title="b6">a</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="b7">x</font> being    <a href="msafree4.html#M1" title="MSAFREE4:mode.1">Element</a> of  the <a href="aofa_a00.html#U4" title="AOFA_A00:sel.4">generators</a> of <font color="Olive" title="b4">G</font> <a href="msafree4.html#K1" title="MSAFREE4:func.1">.</a> <font color="Olive" title="b6">a</font><br/>  for <font color="Olive" title="b8">t</font> being   <a href="msualg_6.html#NM1" title="MSUALG_6:NM.1">Element</a> of <font color="Olive" title="b3">T</font>,<font color="Olive" title="b6">a</font> holds  <font color="Olive" title="b7">x</font> <a href="aofa_a00.html#K11" title="AOFA_A00:func.11">:=</a> (<font color="Olive" title="b8">t</font>,<font color="Olive" title="b5">A</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="aofa_000.html#K18" title="AOFA_000:func.18">ElementaryInstructions</a> <font color="Olive" title="b5">A</font></div></div>
