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<b>set </b><font color="Maroon" title="c2">G</font> =  <a href="comput_1.html#K13" title="COMPUT_1:func.13">(1,2)-&gt;(1,?,2)</a> <font color="Maroon" title="c1">g</font>;<br/>
<a NAME="E1:150_1_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1"><a href="funct_6.html#K6" title="FUNCT_6:func.6">&lt;:</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p3">(<span class="default">3 <a href="comput_1.html#K5" title="COMPUT_1:func.5">proj</a> 1</span>)</span>,<span class="p3">(<span class="default">3 <a href="comput_1.html#K5" title="COMPUT_1:func.5">proj</a> 3</span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="funct_6.html#K6" title="FUNCT_6:func.6">:&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default">3 <a href="comput_1.html#K5" title="COMPUT_1:func.5">proj</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default">3 <a href="comput_1.html#K5" title="COMPUT_1:func.5">proj</a> 3</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_6.html#T62" title="FUNCT_6:th.62">FUNCT_6:62</a></i>;<br/>
<b>then </b><i><font color="Green" title="E99">A1</font></i>:  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1"><a href="funct_6.html#K6" title="FUNCT_6:func.6">&lt;:</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p3">(<span class="default">3 <a href="comput_1.html#K5" title="COMPUT_1:func.5">proj</a> 1</span>)</span>,<span class="p3">(<span class="default">3 <a href="comput_1.html#K5" title="COMPUT_1:func.5">proj</a> 3</span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="funct_6.html#K6" title="FUNCT_6:func.6">:&gt;</a></span> = 
<span class="p1">(<span class="default">3 <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>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default">3 <a href="comput_1.html#K5" title="COMPUT_1:func.5">proj</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="comput_1.html#T40" target="_self" title="COMPUT_1:th.40">Th40</a></i>
<br/>.= 
<span class="p1">(<span class="default">3 <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>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default">3 <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>)</span>
<b>by </b><i><a class="ref" href="comput_1.html#T40" target="_self" title="COMPUT_1:th.40">Th40</a></i>
<br/>.= 
3 <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/>
<a NAME="E3:150_1_1"/><i><font color="Green" title="E100">A2</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="comput_1.html#K13" title="COMPUT_1:func.13">(1,2)-&gt;(1,?,2)</a> <font color="Maroon" title="c1">g</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1"><a href="funct_6.html#K6" title="FUNCT_6:func.6">&lt;:</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p3">(<span class="default">3 <a href="comput_1.html#K5" title="COMPUT_1:func.5">proj</a> 1</span>)</span>,<span class="p3">(<span class="default">3 <a href="comput_1.html#K5" title="COMPUT_1:func.5">proj</a> 3</span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="funct_6.html#K6" title="FUNCT_6:func.6">:&gt;</a></span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T44" title="RELAT_1:th.44">RELAT_1:44</a></i>;<br/>
<a NAME="E4:150_1_1"/>
3 <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="tarski.html#R1" title="TARSKI:pred.1">c=</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> 
 
<b>by </b><i><a class="ref" href="msualg_1.html#T12" title="MSUALG_1:th.12">MSUALG_1:12</a></i>;<br/>
<a NAME="E5:150_1_1"/><b>then </b><i><font color="Green" title="E101">A3</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="comput_1.html#K13" title="COMPUT_1:func.13">(1,2)-&gt;(1,?,2)</a> <font color="Maroon" title="c1">g</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> 
 
<b>by </b><i><a class="txt" href="#E2:150_1_1"><i><font color="Green" title="E99">A1</font></i></a>, <a class="txt" href="#E3:150_1_1"><i><font color="Green" title="E100">A2</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<b>thus </b><a NAME="E6:150_1_1"/>
(  <a href="comput_1.html#K13" title="COMPUT_1:func.13">(1,2)-&gt;(1,?,2)</a> <font color="Maroon" title="c1">g</font> is <a href="valued_0.html#V6" title="VALUED_0:attr.6">to-naturals</a> &amp;  <a href="comput_1.html#K13" title="COMPUT_1:func.13">(1,2)-&gt;(1,?,2)</a> <font color="Maroon" title="c1">g</font> is <a href="comput_1.html#V2" title="COMPUT_1:attr.2">from-natural-fseqs</a> )
 <b>by </b><i><a class="txt" href="#E5:150_1_1"><i><font color="Green" title="E101">A3</font></i></a>, <a class="ref" href="comput_1.html#D2" target="_self" title="COMPUT_1:def.2">Def2</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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