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

<b>set </b><font color="Maroon" title="c4">n</font> = <span class="p1">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c1">f1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1;<br/>
<b>reconsider </b><font color="Maroon" title="c5">ff1</font> = <font color="Maroon" title="c1">f1</font>, <font color="Maroon" title="c6">ff2</font> = <font color="Maroon" title="c2">f2</font> as    <a href="rfunct_3.html#M2" title="RFUNCT_3:mode.2">Element</a> of  <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="comput_1.html#T31" target="_self" title="COMPUT_1:th.31">Th31</a></i>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ) <b>-&gt; </b>   <a href="rfunct_3.html#M2" title="RFUNCT_3:mode.2">Element</a> of  <a href="comput_1.html#K3" title="COMPUT_1:func.3">HFuncs</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  =  <a href="comput_1.html#K7" title="COMPUT_1:func.7">primrec</a> <font color="Maroon" title="c1">f1</font>,<font color="Maroon" title="c2">f2</font>,<font color="Maroon" title="c3">i</font>,$1;<br/>
<b>consider </b><font color="Maroon" title="c7">G</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c1">f1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <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> , <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> such that </b><br/><a NAME="E3:96_1_1"/><i><font color="Green" title="E59">A1</font></i>: 
for <font color="Olive" title="b1">p</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c1">f1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <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>  holds  <font color="Maroon" title="c7">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">p</font>)
 <b>from </b><i><a class="ref" href="funct_2.html#S4" title="FUNCT_2:sch.4">FUNCT_2:sch 4</a>();<br/></i>
<b>consider </b><font color="Maroon" title="c8">np</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c1">f1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <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> ;<br/>
<b>reconsider </b><font color="Maroon" title="c9">Y</font> =  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c7">G</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="comput_1.html#K3" title="COMPUT_1:func.3">HFuncs</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span> <b>by </b><i><a class="ref" href="relset_1.html#T12" title="RELSET_1:th.12">RELSET_1:12</a></i>;<br/>
<a NAME="E6:96_1_1"/>
<font color="Maroon" title="c9">Y</font> is    <a href="rfunct_3.html#M1" title="RFUNCT_3:mode.1">PartFunc-set</a> of <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> , <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="96_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c10">f</font> be    <a href="comput_1.html#M1" title="COMPUT_1:mode.1">Element</a> of <font color="Maroon" title="c9">Y</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="rfunct_3.html#D3" title="RFUNCT_3:def.3">RFUNCT_3:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c10">f</font> is    <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> , <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span><br/>

<b>thus </b><a NAME="E1:96_1_1_1"/>
<font color="Maroon" title="c10">f</font> is   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> , <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c10">Y</font> = <font color="Maroon" title="c9">Y</font> as   <a href="rfunct_3.html#NM2" title="RFUNCT_3:NM.2">PFUNC_DOMAIN</a> of <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> , <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ;<br/>
<a NAME="E8:96_1_1"/><i><font color="Green" title="E60">A2</font></i>: 
<font color="Maroon" title="c10">Y</font> is <a href="comput_1.html#V1" title="COMPUT_1:attr.1">compatible</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="96_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c11">f</font>, <font color="Maroon" title="c12">g</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>; <i><font color="Red">:: according to </font></i><a class="ref" href="comput_1.html#D1" target="_self" title="COMPUT_1:def.1">COMPUT_1:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c11">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">Y</font> &amp; <font color="Maroon" title="c12">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">Y</font> implies <font color="Maroon" title="c11">f</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Maroon" title="c12">g</font> )</span><br/>

<b>assume </b><a NAME="E1:96_1_1_2"/>
<font color="Maroon" title="c11">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">Y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c12">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">Y</font> or <font color="Maroon" title="c11">f</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Maroon" title="c12">g</font> )</span><br/>

<b>then consider </b><font color="Maroon" title="c13">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:96_1_1_2"/><i><font color="Green" title="E61">A3</font></i>: 
( <font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c7">G</font> &amp; <font color="Maroon" title="c11">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">x</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>assume </b><a NAME="E4:96_1_1_2"/>
<font color="Maroon" title="c12">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">Y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c11">f</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Maroon" title="c12">g</font></span><br/>

<b>then consider </b><font color="Maroon" title="c14">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E6:96_1_1_2"/><i><font color="Green" title="E62">A4</font></i>: 
( <font color="Maroon" title="c14">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c7">G</font> &amp; <font color="Maroon" title="c12">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">y</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c15">x</font> = <font color="Maroon" title="c13">x</font>, <font color="Maroon" title="c16">y</font> = <font color="Maroon" title="c14">y</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c1">f1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <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="comput_1.html#E3:96_1_1_2"><i><font color="Green" title="E61">A3</font></i></a>, <a class="txt" href="comput_1.html#E6:96_1_1_2"><i><font color="Green" title="E62">A4</font></i></a></i>;<br/>
<a NAME="E8:96_1_1_2"/>
( <font color="Maroon" title="c11">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="comput_1.html#K7" title="COMPUT_1:func.7">primrec</a> <font color="Maroon" title="c5">ff1</font>,<font color="Maroon" title="c6">ff2</font>,<font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c15">x</font> &amp; <font color="Maroon" title="c12">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="comput_1.html#K7" title="COMPUT_1:func.7">primrec</a> <font color="Maroon" title="c5">ff1</font>,<font color="Maroon" title="c6">ff2</font>,<font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c16">y</font> )
 
<b>by </b><i><a class="txt" href="comput_1.html#E3:96_1_1"><i><font color="Green" title="E59">A1</font></i></a>, <a class="txt" href="comput_1.html#E3:96_1_1_2"><i><font color="Green" title="E61">A3</font></i></a>, <a class="txt" href="comput_1.html#E6:96_1_1_2"><i><font color="Green" title="E62">A4</font></i></a></i>;<br/>
<b>hence </b><a NAME="E9:96_1_1_2"/>
<font color="Maroon" title="c11">f</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Maroon" title="c12">g</font>
 <b>by </b><i><a class="ref" href="comput_1.html#T55" target="_self" title="COMPUT_1:th.55">Th55</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="96_1_1_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c11">x</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c1">f1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">x</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c1">f1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <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><br/><a NAME="E1:96_1_1_3"/>
<font color="Maroon" title="c7">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="comput_1.html#K7" title="COMPUT_1:func.7">primrec</a> <font color="Maroon" title="c5">ff1</font>,<font color="Maroon" title="c6">ff2</font>,<font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c11">x</font>
 <b>by </b><i><a class="txt" href="comput_1.html#E3:96_1_1"><i><font color="Green" title="E59">A1</font></i></a></i>;<br/><b>hence </b><a NAME="E2:96_1_1_3"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">x</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c1">f1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <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="ref" href="comput_1.html#T56" target="_self" title="COMPUT_1:th.56">Th56</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>then consider </b><font color="Maroon" title="c11">g</font> being    <a href="rfunct_3.html#M2" title="RFUNCT_3:mode.2">Element</a> of  <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> such that </b><br/><a NAME="E11:96_1_1"/><i><font color="Green" title="E61">A5</font></i>: 
( <font color="Maroon" title="c11">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <font color="Maroon" title="c7">G</font> &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c11">g</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c1">f1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <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="comput_1.html#E8:96_1_1"><i><font color="Green" title="E60">A2</font></i></a>, <a class="ref" href="comput_1.html#T43" target="_self" title="COMPUT_1:th.43">Th43</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c11">g</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">G</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c1">f1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <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> , <a href="comput_1.html#K3" title="COMPUT_1:func.3">HFuncs</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>( <font color="Maroon" title="c11">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <font color="Olive" title="b1">G</font> &amp; ( for <font color="Olive" title="b2">p</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c1">f1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <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>  holds  <font color="Olive" title="b1">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="comput_1.html#K7" title="COMPUT_1:func.7">primrec</a> <font color="Maroon" title="c1">f1</font>,<font color="Maroon" title="c2">f2</font>,<font color="Maroon" title="c3">i</font>,<font color="Olive" title="b2">p</font> ) )</span><br/>

<b>take </b>
<font color="Maroon" title="c7">G</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c11">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <font color="Maroon" title="c7">G</font> &amp; ( for <font color="Olive" title="b1">p</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c1">f1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <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>  holds  <font color="Maroon" title="c7">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="comput_1.html#K7" title="COMPUT_1:func.7">primrec</a> <font color="Maroon" title="c1">f1</font>,<font color="Maroon" title="c2">f2</font>,<font color="Maroon" title="c3">i</font>,<font color="Olive" title="b1">p</font> ) )</span><br/>

<b>thus </b><a NAME="E12:96_1_1"/>
( <font color="Maroon" title="c11">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <font color="Maroon" title="c7">G</font> &amp; ( for <font color="Olive" title="b1">p</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c1">f1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <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>  holds  <font color="Maroon" title="c7">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="comput_1.html#K7" title="COMPUT_1:func.7">primrec</a> <font color="Maroon" title="c1">f1</font>,<font color="Maroon" title="c2">f2</font>,<font color="Maroon" title="c3">i</font>,<font color="Olive" title="b1">p</font> ) )
 <b>by </b><i><a class="txt" href="comput_1.html#E3:96_1_1"><i><font color="Green" title="E59">A1</font></i></a>, <a class="txt" href="comput_1.html#E11:96_1_1"><i><font color="Green" title="E61">A5</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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