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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E76">Th75</font></span>: <a NAME="T75"><span class="comment"><font color="firebrick">:: AOFA_000:75</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>  st <font color="Olive" title="b1">A</font> is  <a href="freealg.html#V3" title="FREEALG:attr.3">free</a>  holds <br/> for <font color="Olive" title="b2">C</font>, <font color="Olive" title="b3">I</font>, <font color="Olive" title="b4">D</font>, <font color="Olive" title="b5">J</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">A</font> holds <br/> (  <a href="aofa_000.html#K16" title="AOFA_000:func.16">while</a> (<font color="Olive" title="b2">C</font>,<font color="Olive" title="b3">I</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">C</font> &amp;  <a href="aofa_000.html#K16" title="AOFA_000:func.16">while</a> (<font color="Olive" title="b2">C</font>,<font color="Olive" title="b3">I</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">I</font> &amp; (  <a href="aofa_000.html#K16" title="AOFA_000:func.16">while</a> (<font color="Olive" title="b2">C</font>,<font color="Olive" title="b3">I</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aofa_000.html#K16" title="AOFA_000:func.16">while</a> (<font color="Olive" title="b4">D</font>,<font color="Olive" title="b5">J</font>) implies ( <font color="Olive" title="b2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">D</font> &amp; <font color="Olive" title="b3">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">J</font> ) ) )</div></div>
