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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E66">Th63</font></span>: <a NAME="T64"><span class="comment"><font color="firebrick">:: COMPUT_1:64</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive" title="b2">f1</font>, <font color="Olive" title="b3">f2</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>   <a href="comput_1.html#NV2" title="COMPUT_1:NV.2">to-naturals</a>   <a href="margrel1.html#V2" title="MARGREL1:attr.2">homogeneous</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <span class="p1">(<span class="default"><a href="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Olive" title="b2">f1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Olive" title="b3">f2</font> &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">i</font> &amp; <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Olive" title="b2">f1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 holds <br/> <a href="comput_1.html#K7" title="COMPUT_1:func.7">primrec</a> (<font color="Olive" title="b2">f1</font>,<font color="Olive" title="b3">f2</font>,<font color="Olive" title="b1">i</font>) <a href="comput_1.html#R1" title="COMPUT_1:pred.1">is_primitive-recursively_expressed_by</a> <font color="Olive" title="b2">f1</font>,<font color="Olive" title="b3">f2</font>,<font color="Olive" title="b1">i</font></div></div>
