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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E85">Th83</font></span>: <a NAME="T83"><span class="comment"><font color="firebrick">:: AOFA_000:83</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font> being   <a href="aofa_000.html#NM1" title="AOFA_000:NM.1">preIfWhileAlgebra</a><br/>  for <font color="Olive" title="b2">I</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">A</font><br/>  for <font color="Olive" title="b3">S</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b4">T</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b3">S</font><br/>  for <font color="Olive" title="b5">s</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b3">S</font><br/>  for <font color="Olive" title="b6">f</font> being    <a href="aofa_000.html#M1" title="AOFA_000:mode.1">ExecutionFunction</a> of <font color="Olive" title="b1">A</font>,<font color="Olive" title="b3">S</font>,<font color="Olive" title="b4">T</font>  st <font color="Olive" title="b5">s</font> <a href="aofa_000.html#NR1" title="AOFA_000:NR.1">nin</a> <font color="Olive" title="b4">T</font> holds <br/>( <font color="Olive" title="b6">f</font> <a href="aofa_000.html#R4" title="AOFA_000:pred.4">iteration_terminates_for</a> <font color="Olive" title="b2">I</font>,<font color="Olive" title="b5">s</font> &amp;  <a href="aofa_000.html#K20" title="AOFA_000:func.20">iteration-degree</a> (<font color="Olive" title="b2">I</font>,<font color="Olive" title="b5">s</font>,<font color="Olive" title="b6">f</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )</div></div>
