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<b>reconsider </b><font color="Maroon" title="c3">g</font> = <font color="Maroon" title="c1">g</font>, <font color="Maroon" title="c4">h</font> = <font color="Maroon" title="c2">h</font> as    <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>  <b>by </b><i><a class="ref" href="comput_1.html#D19" target="_self" title="COMPUT_1:def.19">Def19</a></i>;<br/>
<a NAME="E2:161_1_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">g</font>,<font color="Maroon" title="c4">h</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="comput_1.html#K9" title="COMPUT_1:func.9">PrimRec</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4" title="FINSEQ_1:def.4">FINSEQ_1:def 4</a></i>;<br/>
<a NAME="E3:161_1_1"/><b>then </b><i><font color="Green" title="E103">A1</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">g</font>,<font color="Maroon" title="c4">h</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="comput_1.html#K3" title="COMPUT_1:func.3">HFuncs</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E4:161_1_1"/><i><font color="Green" title="E104">A2</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">g</font>,<font color="Maroon" title="c4">h</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">g</font>,<font color="Maroon" title="c4">h</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<b>by </b><i><a class="ref" href="finseq_2.html#T147" title="FINSEQ_2:th.147">FINSEQ_2:147</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="161_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">f1</font>, <font color="Maroon" title="c6">f2</font> be  <a href="unialg_1.html#V1" title="UNIALG_1:attr.1">homogeneous</a> <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>;<br/><b>assume </b><a NAME="E1:161_1_1_1"/>
( <font color="Maroon" title="c5">f1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">g</font>,<font color="Maroon" title="c4">h</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> &amp; <font color="Maroon" title="c6">f2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">g</font>,<font color="Maroon" title="c4">h</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> )
 ;<br/><a NAME="E2:161_1_1_1"/><b>then </b>
( ( <font color="Maroon" title="c5">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g</font> or <font color="Maroon" title="c5">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h</font> ) &amp; ( <font color="Maroon" title="c6">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g</font> or <font color="Maroon" title="c6">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h</font> ) )
 <b>by </b><i><a class="txt" href="comput_1.html#E4:161_1_1"><i><font color="Green" title="E104">A2</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><a NAME="E3:161_1_1_1"/><b>then </b>
(  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c5">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp;  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c6">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 )
 <b>by </b><i><a class="ref" href="comput_1.html#D26" target="_self" title="COMPUT_1:def.26">Def26</a></i>;<br/><b>hence </b><a NAME="E4:161_1_1_1"/>
 <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c5">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c6">f2</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:161_1_1"/>
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">g</font>,<font color="Maroon" title="c2">h</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> is <a href="comput_1.html#V4" title="COMPUT_1:attr.4">with_the_same_arity</a>
 <b>by </b><i><a class="txt" href="comput_1.html#E3:161_1_1"><i><font color="Green" title="E103">A1</font></i></a>, <a class="ref" href="comput_1.html#T33" target="_self" title="COMPUT_1:th.33">Th33</a></i>;<br/>


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