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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E88">Th88</font></span>: <a NAME="T88"><span class="comment"><font color="firebrick">:: AOFA_000:88</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font> being   <a href="freealg.html#V3" title="FREEALG:attr.3">free</a>  <a href="aofa_000.html#NM1" title="AOFA_000:NM.1">preIfWhileAlgebra</a><br/>  for <font color="Olive" title="b2">I1</font>, <font color="Olive" title="b3">I2</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="b4">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b2">I1</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Olive" title="b3">I2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="aofa_000.html#K18" title="AOFA_000:func.18">ElementaryInstructions</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="aofa_000.html#K9" title="AOFA_000:func.9">|^</a> <font color="Olive" title="b4">n</font> holds <br/> ex <font color="Olive" title="b5">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <br/>( <font color="Olive" title="b4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &amp; <font color="Olive" title="b2">I1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="aofa_000.html#K18" title="AOFA_000:func.18">ElementaryInstructions</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="aofa_000.html#K9" title="AOFA_000:func.9">|^</a> <font color="Olive" title="b5">i</font> &amp; <font color="Olive" title="b3">I2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="aofa_000.html#K18" title="AOFA_000:func.18">ElementaryInstructions</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="aofa_000.html#K9" title="AOFA_000:func.9">|^</a> <font color="Olive" title="b5">i</font> )</div></div>
