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<a NAME="E1:147_1_1"/><span class="lab"><font color="Green" title="E92">A1</font></span>: 
<font color="Maroon" title="c2">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="comput_1.html#K9" title="COMPUT_1:func.9">PrimRec</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="comput_1.html#D19" target="_self" title="COMPUT_1:def.19">Def19</a></span>;<br/>
<a NAME="E2:147_1_1"/><span class="lab"><font color="Green" title="E93">A2</font></span>: 
 <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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="comput_1.html#D24" target="_self" title="COMPUT_1:def.24">Def24</a></span>;<br/>
<a NAME="E3:147_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#K9" title="COMPUT_1:func.9">PrimRec</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="comput_1.html#D19" target="_self" title="COMPUT_1:def.19">Def19</a></span>;<br/>
<span class="kw">then </span> <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> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:147_1_1"><span class="lab"><font color="Green" title="E93">A2</font></span></a>, <a class="ref" href="comput_1.html#T25" target="_self" title="COMPUT_1:th.25">Th25</a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T112" title="FINSEQ_2:th.112">FINSEQ_2:112</a></span>
;<br/>
<a NAME="E5:147_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E94">A3</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E6:147_1_1"/><span class="lab"><font color="Green" title="E95">A4</font></span>: 
<font color="Maroon" title="c1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="comput_1.html#K9" title="COMPUT_1:func.9">PrimRec</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="comput_1.html#D19" target="_self" title="COMPUT_1:def.19">Def19</a></span>;<br/>
<a NAME="E7:147_1_1"/><span class="lab"><font color="Green" title="E96">A5</font></span>: 
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
 
;<br/>
<a NAME="E8:147_1_1"/>
 <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
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="comput_1.html#D26" target="_self" title="COMPUT_1:def.26">Def26</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:147_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#K9" title="COMPUT_1:func.9">PrimRec</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:147_1_1"><span class="lab"><font color="Green" title="E96">A5</font></span></a>, <a class="txt" href="#E2:147_1_1"><span class="lab"><font color="Green" title="E93">A2</font></span></a>, <a class="txt" href="#E6:147_1_1"><span class="lab"><font color="Green" title="E95">A4</font></span></a>, <a class="txt" href="#E1:147_1_1"><span class="lab"><font color="Green" title="E92">A1</font></span></a>, <a class="ref" href="comput_1.html#T77" target="_self" title="COMPUT_1:th.77">Th77</a></span>; <span class="comment"><font color="Red">:: according to </font></span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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#V9" title="COMPUT_1:attr.9">unary</a> </span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c3">ii</font> = <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of 1 <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>  <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T151" title="FINSEQ_2:th.151">FINSEQ_2:151</a></span>;<br/>
<a NAME="E11:147_1_1"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&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>
 
<span class="kw">by</span> <span class="lab"><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></span>;<br/>
<a NAME="E12:147_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E97">A6</font></span>: 
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="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E13:147_1_1"/>
 <a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="wsierp_1.html#T26" title="WSIERP_1:th.26">WSIERP_1:26</a></span>;<br/>
<a NAME="E14:147_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">ii</font> <a href="comput_1.html#K8" title="COMPUT_1:func.8">+*</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#K1" title="RELSET_1:func.1">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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:147_1_1"><span class="lab"><font color="Green" title="E96">A5</font></span></a>, <a class="txt" href="#E2:147_1_1"><span class="lab"><font color="Green" title="E93">A2</font></span></a>, <a class="txt" href="#E5:147_1_1"><span class="lab"><font color="Green" title="E94">A3</font></span></a>, <a class="txt" href="#E12:147_1_1"><span class="lab"><font color="Green" title="E97">A6</font></span></a>, <a class="txt" href="comput_1.html#E81"><span class="lab"><font color="Green" title="E65">Lm6</font></span></a></span>;<br/>
<a NAME="E15:147_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E98">A7</font></span>: 
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T97" title="FUNCT_7:th.97">FUNCT_7:97</a></span>;<br/>
<a NAME="E16:147_1_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T56" title="FINSEQ_1:th.56">FINSEQ_1:56</a></span>;<br/>
<span class="kw">hence </span><a NAME="E17:147_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
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:147_1_1"><span class="lab"><font color="Green" title="E98">A7</font></span></a>, <a class="ref" href="unialg_1.html#D10" title="UNIALG_1:def.10">UNIALG_1:def 10</a></span>; <span class="comment"><font color="Red">:: according to </font></span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
