<?xml version="1.0"?>
<div class="add">

<a NAME="E1:142_1_1"/><i><font color="Green" title="E94">A1</font></i>: 
(  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp;  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2 &amp; <font color="Maroon" title="c1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="comput_1.html#K8" title="COMPUT_1:func.8">PrimRec</a>  &amp; <font color="Maroon" title="c2">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="comput_1.html#K8" title="COMPUT_1:func.8">PrimRec</a>  )
 
<b>by </b><i><a class="ref" href="comput_1.html#D19" target="_self" title="COMPUT_1:def.19">Def19</a>, <a class="ref" href="comput_1.html#D24" target="_self" title="COMPUT_1:def.24">Def24</a>, <a class="ref" href="comput_1.html#D26" target="_self" title="COMPUT_1:def.26">Def26</a></i>;<br/>
<b>hence </b><a NAME="E2:142_1_1"/>
 <a href="comput_1.html#K7" title="COMPUT_1:func.7">primrec</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font>,1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="comput_1.html#K8" title="COMPUT_1:func.8">PrimRec</a> 
 <b>by </b><i><a class="ref" href="comput_1.html#T77" target="_self" title="COMPUT_1:th.77">Th77</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="comput_1.html#D19" target="_self" title="COMPUT_1:def.19">COMPUT_1:def 19</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="comput_1.html#K7" title="COMPUT_1:func.7">primrec</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font>,1 is <a href="comput_1.html#V10" title="COMPUT_1:attr.10">unary</a></span><br/>

<a NAME="E3:142_1_1"/><i><font color="Green" title="E95">A2</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">1</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="finseq_1.html#T55" title="FINSEQ_1:th.55">FINSEQ_1:55</a></i>;<br/>
<a NAME="E4:142_1_1"/>
<font color="Maroon" title="c1">f</font> is    <a href="comput_1.html#M1" title="COMPUT_1:mode.1">Element</a> of  <a href="comput_1.html#K8" title="COMPUT_1:func.8">PrimRec</a> 
 
<b>by </b><i><a class="ref" href="comput_1.html#D19" target="_self" title="COMPUT_1:def.19">Def19</a></i>;<br/>
<b>then </b> <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">f</font> = 
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
<b>by </b><i><a class="txt" href="#E1:142_1_1"><i><font color="Green" title="E94">A1</font></i></a>, <a class="ref" href="comput_1.html#T25" target="_self" title="COMPUT_1:th.25">Th25</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<b>by </b><i><a class="ref" href="finseq_2.html#T112" title="FINSEQ_2:th.112">FINSEQ_2:112</a></i>
;<br/>
<a NAME="E6:142_1_1"/><b>then </b>
(  <a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <span class="p1"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span>,1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">f</font> &amp; 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span> )
 
<b>by </b><i><a class="txt" href="#E3:142_1_1"><i><font color="Green" title="E95">A2</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a>, <a class="ref" href="wsierp_1.html#T26" title="WSIERP_1:th.26">WSIERP_1:26</a></i>;<br/>
<a NAME="E7:142_1_1"/><b>then </b>
<span class="p1"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span> <a href="midsp_3.html#K1" title="MIDSP_3:func.1">+*</a> 1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="comput_1.html#K7" title="COMPUT_1:func.7">primrec</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font>,1</span>)</span>
 
<b>by </b><i><a class="txt" href="#E1:142_1_1"><i><font color="Green" title="E94">A1</font></i></a>, <a class="txt" href="comput_1.html#E81"><i><font color="Green" title="E67">Lm6</font></i></a></i>;<br/>
<a NAME="E8:142_1_1"/><b>then </b>
( <span class="p1"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="comput_1.html#K7" title="COMPUT_1:func.7">primrec</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font>,1</span>)</span> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T56" title="FINSEQ_1:th.56">FINSEQ_1:56</a>, <a class="ref" href="funct_7.html#T97" title="FUNCT_7:th.97">FUNCT_7:97</a></i>;<br/>
<b>hence </b><a NAME="E9:142_1_1"/>
 <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <span class="p1">(<span class="default"><a href="comput_1.html#K7" title="COMPUT_1:func.7">primrec</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font>,1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>by </b><i><a class="ref" href="unialg_1.html#D10" title="UNIALG_1:def.10">UNIALG_1:def 10</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="comput_1.html#D25" target="_self" title="COMPUT_1:def.25">COMPUT_1:def 25</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
