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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E79">Def20</font></span>   defines <a href="comput_1.html#K13" title="COMPUT_1:func.13">PrimRec-Approximation</a> <a onclick="hs(this)" href="javascript:()">COMPUT_1:def 20 : <br/></a><span> for <font color="Olive">b<sub>1</sub></font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">sequence</a> of <span class="p1">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <span class="p2">(<span class="default"><a href="comput_1.html#K2" title="COMPUT_1:func.2">HFuncs</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a></span>)</span></span>)</span> holds <br/> ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="comput_1.html#K13" title="COMPUT_1:func.13">PrimRec-Approximation</a>  iff ( <font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="comput_1.html#K10" title="COMPUT_1:func.10">initial-funcs</a>  &amp; (  for <font color="Olive" title="b2">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="comput_1.html#K11" title="COMPUT_1:func.11">PR-closure</a> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b2">m</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="comput_1.html#K12" title="COMPUT_1:func.12">composition-closure</a> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b2">m</font></span>)</span></span>)</span> ) ) );<br/></span></div>
