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<b>set </b><font color="Maroon">c<sub>1</sub></font> =  <a href="comput_1.html#K5" target="_self">HFuncs</a> <a href="numbers.html#K5">NAT</a> ;<br/>
<b>thus </b><a NAME="E1:114"/>
( 0 <a href="comput_1.html#K6" target="_self">const</a> 0 <a href="hidden.html#R2">in</a>  <a href="comput_1.html#K5" target="_self">HFuncs</a> <a href="numbers.html#K5">NAT</a>  &amp; 1 <a href="comput_1.html#K7" target="_self">succ</a> 1 <a href="hidden.html#R2">in</a>  <a href="comput_1.html#K5" target="_self">HFuncs</a> <a href="numbers.html#K5">NAT</a>  &amp; ( for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="comput_1.html#K8" target="_self">proj</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="comput_1.html#K5" target="_self">HFuncs</a> <a href="numbers.html#K5">NAT</a>  ) )
 <b>by </b><i><a class="ref" href="comput_1.html#T34" target="_self">Th34</a>, <a class="ref" href="comput_1.html#T37" target="_self">Th37</a>, <a class="ref" href="comput_1.html#T39" target="_self">Th39</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="comput_1.html#D17" target="_self">COMPUT_1:def 17</a><br/>

<b>thus </b><a NAME="E2:114"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="rfunct_3.html#M2">Element</a> of  <a href="comput_1.html#K5" target="_self">HFuncs</a> <a href="numbers.html#K5">NAT</a> <br/>for <font color="Olive">b<sub>2</sub></font> being <a href="comput_1.html#V5" target="_self">with_the_same_arity</a>  <a href="finseq_1.html#M2">FinSequence</a> of  <a href="comput_1.html#K5" target="_self">HFuncs</a> <a href="numbers.html#K5">NAT</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="comput_1.html#K5" target="_self">HFuncs</a> <a href="numbers.html#K5">NAT</a>  &amp;  <a href="comput_1.html#K3" target="_self">arity</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Olive">b<sub>2</sub></font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Olive">b<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="comput_1.html#K5" target="_self">HFuncs</a> <a href="numbers.html#K5">NAT</a>  holds <br/><font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1"><a href="funct_6.html#K6">&lt;:</a><span class="default"><font color="Olive">b<sub>2</sub></font></span><a href="funct_6.html#K6">:&gt;</a></span> <a href="hidden.html#R2">in</a>  <a href="comput_1.html#K5" target="_self">HFuncs</a> <a href="numbers.html#K5">NAT</a> 
 <b>by </b><i><a class="ref" href="comput_1.html#T46" target="_self">Th46</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="comput_1.html#D15" target="_self">COMPUT_1:def 15</a><br/>

<b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="rfunct_3.html#M2">Element</a> of  <a href="comput_1.html#K5" target="_self">HFuncs</a> <a href="numbers.html#K5">NAT</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="comput_1.html#D16" target="_self">COMPUT_1:def 16</a><br/>

<b>thus </b><a NAME="E3:114"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="rfunct_3.html#M2">Element</a> of  <a href="comput_1.html#K5" target="_self">HFuncs</a> <a href="numbers.html#K5">NAT</a> <br/>for <font color="Olive">b<sub>3</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">c<sub>2</sub></font> <a href="comput_1.html#R1" target="_self">is_primitive-recursively_expressed_by</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="comput_1.html#K5" target="_self">HFuncs</a> <a href="numbers.html#K5">NAT</a>  &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="comput_1.html#K5" target="_self">HFuncs</a> <a href="numbers.html#K5">NAT</a>  holds <br/><font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="comput_1.html#K5" target="_self">HFuncs</a> <a href="numbers.html#K5">NAT</a> 
 ;<br/>


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