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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be  <a href="seqm_3.html#V6">to-naturals</a> <a href="comput_1.html#V2" target="_self">from-natural-fseqs</a> <a href="comput_1.html#V3" target="_self">len-total</a> <a href="comput_1.html#V4" target="_self">homogeneous</a> <a href="comput_1.html#V12" target="_self">binary</a> <a href="funct_1.html#NM1">Function</a>;<br/>







<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span> as    <a href="finseq_2.html#M2">Element</a> of 3 <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#T124">FINSEQ_2:124</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</sub></font> as  non <a href="xboole_0.html#V1">empty</a> <a href="unialg_1.html#V2">quasi_total</a> <a href="comput_1.html#V4" target="_self">homogeneous</a> <a href="partfun1.html#NM1">PartFunc</a> of <a href="numbers.html#K5">NAT</a>  <a href="finseq_2.html#K3">*</a> , <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="comput_1.html#T20" target="_self">Th20</a></i>;<br/>
<a NAME="E3:157"/><i><font color="Green">E103</font></i>: 
 <a href="comput_1.html#K3" target="_self">arity</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 2
 
<b>by </b><i><a class="ref" href="comput_1.html#D26" target="_self">Def26</a></i>;<br/>
<a NAME="E4:157"/><b>then </b><i><font color="Green">E104</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></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#K10">&lt;*</a><span class="default"><span class="p4">(<span class="default">3 <a href="comput_1.html#K8" target="_self">proj</a> 1</span>)</span>,<span class="p4">(<span class="default">3 <a href="comput_1.html#K8" target="_self">proj</a> 3</span>)</span></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="funct_6.html#K6">:&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> 3 <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i><a class="txt" href="comput_1.html#E121"><i><font color="Green">Lemma101</font></i></a></i>;<br/>
<a NAME="E5:157"/><i><font color="Green">E105</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="funct_6.html#K6">&lt;:</a><span class="default"><span class="p2"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><span class="p3">(<span class="default">3 <a href="comput_1.html#K8" target="_self">proj</a> 1</span>)</span>,<span class="p3">(<span class="default">3 <a href="comput_1.html#K8" target="_self">proj</a> 3</span>)</span></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="funct_6.html#K6">:&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default">3 <a href="comput_1.html#K8" target="_self">proj</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default">3 <a href="comput_1.html#K8" target="_self">proj</a> 3</span>)</span></span>)</span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="funct_6.html#K6">&lt;:</a><span class="default"><span class="p2"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><span class="p3">(<span class="default">3 <a href="comput_1.html#K8" target="_self">proj</a> 1</span>)</span>,<span class="p3">(<span class="default">3 <a href="comput_1.html#K8" target="_self">proj</a> 3</span>)</span></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="funct_6.html#K6">:&gt;</a></span> <a href="hidden.html#R1">=</a> 3 <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a>  )
 
<b>by </b><i><a class="txt" href="comput_1.html#E3:157"><i><font color="Green">E103</font></i></a>, <a class="txt" href="comput_1.html#E121"><i><font color="Green">Lemma101</font></i></a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="comput_1.html#K16" target="_self">(1,2)-&gt;(1,?,2)</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></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#K10">&lt;*</a><span class="default"><span class="p4">(<span class="default">3 <a href="comput_1.html#K8" target="_self">proj</a> 1</span>)</span>,<span class="p4">(<span class="default">3 <a href="comput_1.html#K8" target="_self">proj</a> 3</span>)</span></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="funct_6.html#K6">:&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>

<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2"><a href="funct_6.html#K6">&lt;:</a><span class="default"><span class="p3"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><span class="p4">(<span class="default">3 <a href="comput_1.html#K8" target="_self">proj</a> 1</span>)</span>,<span class="p4">(<span class="default">3 <a href="comput_1.html#K8" target="_self">proj</a> 3</span>)</span></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="funct_6.html#K6">:&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="comput_1.html#E4:157"><i><font color="Green">E104</font></i></a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">3 <a href="comput_1.html#K8" target="_self">proj</a> 1</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">3 <a href="comput_1.html#K8" target="_self">proj</a> 3</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="finseq_1.html#K10">*&gt;</a></span>
<b>by </b><i><a class="txt" href="comput_1.html#E5:157"><i><font color="Green">E105</font></i></a>, <a class="ref" href="funct_6.html#T62">FUNCT_6:62</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="comput_1.html#K2" target="_self">.</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">3 <a href="comput_1.html#K8" target="_self">proj</a> 3</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="finseq_1.html#K10">*&gt;</a></span>
<b>by </b><i><a class="ref" href="comput_1.html#T42" target="_self">Th42</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="comput_1.html#K2" target="_self">.</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="comput_1.html#K2" target="_self">.</a> 3</span>)</span></span><a href="finseq_4.html#K2">*&gt;</a></span>
<b>by </b><i><a class="ref" href="comput_1.html#T42" target="_self">Th42</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="comput_1.html#K2" target="_self">.</a> 3</span>)</span></span><a href="finseq_4.html#K2">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>


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