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<b>let </b><font color="Maroon" title="c1">i</font>, <font color="Maroon" title="c2">j</font>, <font color="Maroon" title="c3">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c4">f</font> be  <a href="comput_1.html#NV2" title="COMPUT_1:NV.2">to-naturals</a> <a href="unialg_1.html#V1" title="UNIALG_1:attr.1">homogeneous</a> <a href="comput_1.html#V2" title="COMPUT_1:attr.2">from-natural-fseqs</a> <a href="comput_1.html#V3" title="COMPUT_1:attr.3">len-total</a> <a href="comput_1.html#V11" title="COMPUT_1:attr.11">binary</a> <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>;<br/>







<b>reconsider </b><font color="Maroon" title="c5">ijk</font> = <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>,<font color="Maroon" title="c3">k</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of 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>  <b>by </b><i><a class="ref" href="finseq_2.html#T124" title="FINSEQ_2:th.124">FINSEQ_2:124</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">ff</font> = <font color="Maroon" title="c4">f</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="unialg_1.html#V1" title="UNIALG_1:attr.1">homogeneous</a> <a href="unialg_1.html#V2" title="UNIALG_1:attr.2">quasi_total</a> <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>  <b>by </b><i><a class="ref" href="comput_1.html#T20" target="_self" title="COMPUT_1:th.20">Th20</a></i>;<br/>
<a NAME="E3:154"/><i><font color="Green" title="E100">A1</font></i>: 
 <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c6">ff</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/>
<a NAME="E4:154"/><b>then </b><i><font color="Green" title="E101">A2</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">ff</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2"><a href="funct_6.html#K6" title="FUNCT_6:func.6">&lt;:</a><span class="default"><span class="p3"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p4">(<span class="default">3 <a href="comput_1.html#K6" title="COMPUT_1:func.6">proj</a> 1</span>)</span>,<span class="p4">(<span class="default">3 <a href="comput_1.html#K6" title="COMPUT_1:func.6">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>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 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> 
 
<b>by </b><i><a class="txt" href="comput_1.html#E121"><i><font color="Green" title="E98">Lm8</font></i></a></i>;<br/>
<a NAME="E5:154"/><i><font color="Green" title="E102">A3</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#K6" title="COMPUT_1:func.6">proj</a> 1</span>)</span>,<span class="p3">(<span class="default">3 <a href="comput_1.html#K6" title="COMPUT_1:func.6">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#K6" title="COMPUT_1:func.6">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#K6" title="COMPUT_1:func.6">proj</a> 3</span>)</span></span>)</span> &amp;  <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#K6" title="COMPUT_1:func.6">proj</a> 1</span>)</span>,<span class="p3">(<span class="default">3 <a href="comput_1.html#K6" title="COMPUT_1:func.6">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> 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>  )
 
<b>by </b><i><a class="txt" href="comput_1.html#E3:154"><i><font color="Green" title="E100">A1</font></i></a>, <a class="txt" href="comput_1.html#E121"><i><font color="Green" title="E98">Lm8</font></i></a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="comput_1.html#K14" title="COMPUT_1:func.14">(1,2)-&gt;(1,?,2)</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>,<font color="Maroon" title="c3">k</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span> = 
<font color="Maroon" title="c4">f</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2"><a href="funct_6.html#K6" title="FUNCT_6:func.6">&lt;:</a><span class="default"><span class="p3"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p4">(<span class="default">3 <a href="comput_1.html#K6" title="COMPUT_1:func.6">proj</a> 1</span>)</span>,<span class="p4">(<span class="default">3 <a href="comput_1.html#K6" title="COMPUT_1:func.6">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="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">ijk</font></span>)</span>
<b>by </b><i><a class="txt" href="comput_1.html#E4:154"><i><font color="Green" title="E101">A2</font></i></a>, <a class="ref" href="funct_1.html#T22" title="FUNCT_1:th.22">FUNCT_1:22</a></i>
<br/>.= 
<font color="Maroon" title="c4">f</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">3 <a href="comput_1.html#K6" title="COMPUT_1:func.6">proj</a> 1</span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c5">ijk</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">3 <a href="comput_1.html#K6" title="COMPUT_1:func.6">proj</a> 3</span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c5">ijk</font></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
<b>by </b><i><a class="txt" href="comput_1.html#E5:154"><i><font color="Green" title="E102">A3</font></i></a>, <a class="ref" href="funct_6.html#T62" title="FUNCT_6:th.62">FUNCT_6:62</a></i>
<br/>.= 
<font color="Maroon" title="c4">f</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">ijk</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">3 <a href="comput_1.html#K6" title="COMPUT_1:func.6">proj</a> 3</span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c5">ijk</font></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
<b>by </b><i><a class="ref" href="comput_1.html#T42" target="_self" title="COMPUT_1:th.42">Th42</a></i>
<br/>.= 
<font color="Maroon" title="c4">f</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">ijk</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">ijk</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 3</span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
<b>by </b><i><a class="ref" href="comput_1.html#T42" target="_self" title="COMPUT_1:th.42">Th42</a></i>
<br/>.= 
<font color="Maroon" title="c4">f</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c1">i</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">ijk</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 3</span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>
<br/>.= 
<font color="Maroon" title="c4">f</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">k</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>
;<br/>


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