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<b>reconsider </b><font color="Maroon">f'</font> = <font color="Maroon">f</font>, <font color="Maroon">fg</font> = <font color="Maroon">f</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1"><a href="funct_6.html#K6">&lt;:</a><span class="default"><span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">g</font></span><a href="finseq_1.html#K9">*&gt;</a></span></span><a href="funct_6.html#K6">:&gt;</a></span>, <font color="Maroon">g'</font> = <font color="Maroon">g</font> as    <a href="comput_1.html#M1" target="_self">Element</a> of  <a href="comput_1.html#K11" target="_self">PrimRec</a>  <b>by </b><i><a class="ref" href="comput_1.html#T17" target="_self">Th17</a></i>;<br/>
<a NAME="E2:168_1_1"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><font color="Maroon">g'</font></span><a href="binarith.html#K11">*&gt;</a></span> <a href="tarski.html#R1">c=</a>  <a href="comput_1.html#K11" target="_self">PrimRec</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<a NAME="E3:168_1_1"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">g</font></span><a href="finseq_1.html#K9">*&gt;</a></span> <a href="tarski.html#R1">c=</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="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">F</font> = <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><font color="Maroon">g'</font></span><a href="binarith.html#K11">*&gt;</a></span> as  <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>  <b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<a NAME="E5:168_1_1"/><i><font color="Green">E48</font></i>: 
(  <a href="comput_1.html#K3" target="_self">arity</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> 1 &amp;  <a href="comput_1.html#K3" target="_self">arity</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> 2 )
 
<b>by </b><i><a class="ref" href="comput_1.html#T19" target="_self">Th19</a>, </i>;<br/>
<a NAME="E6:168_1_1"/><b>then </b><i><font color="Green">E49</font></i>: 
(  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f'</font> <a href="hidden.html#R1">=</a> 1 <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a>  &amp;  <a href="relset_1.html#K4">dom</a> <font color="Maroon">g'</font> <a href="hidden.html#R1">=</a> 2 <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a>  )
 
<b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">x</font> being    <a href="finseq_2.html#M2">Element</a> of 2 <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a> ;<br/>
<a NAME="E8:168_1_1"/><i><font color="Green">E51</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="funct_6.html#K6">&lt;:</a><span class="default"><font color="Maroon">F</font></span><a href="funct_6.html#K6">:&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font>
 
<b>by </b><i><a class="ref" href="funct_6.html#T61">FUNCT_6:61</a></i>;<br/>
<a NAME="E9:168_1_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="funct_6.html#K6">&lt;:</a><span class="default"><font color="Maroon">F</font></span><a href="funct_6.html#K6">:&gt;</a></span> &amp; <font color="Maroon">g'</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">g'</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">g'</font> <a href="tarski.html#R1">c=</a>  <a href="numbers.html#K5">NAT</a>  )
 
<b>by </b><i>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a>, <a class="ref" href="relset_1.html#T12">RELSET_1:12</a></i>;<br/>
<a NAME="E10:168_1_1"/><b>then </b>
( <span class="p1"><a href="funct_6.html#K6">&lt;:</a><span class="default"><font color="Maroon">F</font></span><a href="funct_6.html#K6">:&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">g'</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font></span>)</span></span><a href="finseq_1.html#K9">*&gt;</a></span> &amp; <font color="Maroon">g'</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a>  )
 
<b>by </b><i>, <a class="ref" href="funct_6.html#T61">FUNCT_6:61</a></i>;<br/>
<a NAME="E11:168_1_1"/><b>then </b>
<span class="p1"><a href="funct_6.html#K6">&lt;:</a><span class="default"><font color="Maroon">F</font></span><a href="funct_6.html#K6">:&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> is    <a href="finseq_2.html#M2">Element</a> of 1 <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i><a class="ref" href="finseq_2.html#T118">FINSEQ_2:118</a></i>;<br/>
<a NAME="E12:168_1_1"/><b>then </b><i><font color="Green">E52</font></i>: 
( not <font color="Maroon">fg</font> is <a href="xboole_0.html#V1">empty</a> &amp; <font color="Maroon">f'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> )
 
<b>by </b><i>, , <a class="ref" href="funct_1.html#T21">FUNCT_1:21</a>, <a class="ref" href="relat_1.html#T60">RELAT_1:60</a></i>;<br/>
<a NAME="E13:168_1_1"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">g</font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T56">FINSEQ_1:56</a></i>;<br/>
<a NAME="E14:168_1_1"/><b>then </b>
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">F</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E15:168_1_1"/><b>then </b>
 <a href="comput_1.html#K4" target="_self">arity</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> 2
 
<b>by </b><i><a class="txt" href="comput_1.html#E30"><i><font color="Green">Lemma106</font></i></a>, </i>;<br/>
<b>hence </b><a NAME="E16:168_1_1"/>
 <a href="comput_1.html#K3" target="_self">arity</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_6.html#K6">&lt;:</a><span class="default"><span class="p3"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">g</font></span><a href="finseq_1.html#K9">*&gt;</a></span></span><a href="funct_6.html#K6">:&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> 2
 <b>by </b><i><a class="ref" href="comput_1.html#T25" target="_self">Th25</a>, <a class="txt" href="comput_1.html#E6:168_1_1"><i><font color="Green">E49</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="comput_1.html#D26" target="_self">COMPUT_1:def 26</a><br/>


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