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<b>let </b><font color="Maroon">f</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="relat_1.html#V2">with_zero</a>  <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">D</font> be  <a href="freealg.html#V1" target="_self">missing_with_Nat</a>  <a href="hidden.html#M1">set</a> ;<br/>



<b>set </b><font color="Maroon">A</font> =  <a href="freealg.html#K3" target="_self">DTConUA</a> <font color="Maroon">f</font>,<font color="Maroon">D</font>;<br/>
<b>set </b><font color="Maroon">AA</font> =  <a href="freealg.html#K15" target="_self">FreeUnivAlgZAO</a> <font color="Maroon">f</font>,<font color="Maroon">D</font>;<br/>
<a NAME="E1:39"/>
0 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font>
 
<b>by </b><i/>;<br/>
<b>then consider </b><font color="Maroon">n</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:39"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> 0 )
 <b>by </b><i><a class="ref" href="finseq_2.html#T11">FINSEQ_2:11</a></i>;<br/>
<a NAME="E4:39"/><i><font color="Green">E49</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="freealg.html#K14" target="_self">FreeOpSeqZAO</a> <font color="Maroon">f</font>,<font color="Maroon">D</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>
 
<b>by </b><i/>;<br/>
<a NAME="E5:39"/><i><font color="Green">E50</font></i>: 
(  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="freealg.html#K14" target="_self">FreeOpSeqZAO</a> <font color="Maroon">f</font>,<font color="Maroon">D</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="freealg.html#K14" target="_self">FreeOpSeqZAO</a> <font color="Maroon">f</font>,<font color="Maroon">D</font></span>)</span></span>)</span> &amp;  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E6:39"/><b>then </b>
the <a href="unialg_1.html#U1">charact</a> of <span class="p1">(<span class="default"><a href="freealg.html#K15" target="_self">FreeUnivAlgZAO</a> <font color="Maroon">f</font>,<font color="Maroon">D</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a>  <a href="freealg.html#K13" target="_self">FreeOpZAO</a> <font color="Maroon">n</font>,<font color="Maroon">f</font>,<font color="Maroon">D</font>
 
<b>by </b><i>, , </i>;<br/>
<b>then reconsider </b><font color="Maroon">o</font> =  <a href="freealg.html#K13" target="_self">FreeOpZAO</a> <font color="Maroon">n</font>,<font color="Maroon">f</font>,<font color="Maroon">D</font> as   <a href="unialg_2.html#NM5">operation</a> of <span class="p1">(<span class="default"><a href="freealg.html#K15" target="_self">FreeUnivAlgZAO</a> <font color="Maroon">f</font>,<font color="Maroon">D</font></span>)</span> <b>by </b><i>, , , <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>take </b>
<font color="Maroon">o</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="unialg_2.html#D12">UNIALG_2:def 12</a><br/>

<a NAME="E8:39"/>
(  <a href="relset_1.html#K4">dom</a> <font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="unialg_1.html#K3">arity</a> <font color="Maroon">o</font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="freealg.html#K15" target="_self">FreeUnivAlgZAO</a> <font color="Maroon">f</font>,<font color="Maroon">D</font></span>)</span> &amp; <font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> &amp;  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="freealg.html#K13" target="_self">FreeOpZAO</a> <font color="Maroon">n</font>,<font color="Maroon">f</font>,<font color="Maroon">D</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">n</font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K4">TS</a> <span class="p2">(<span class="default"><a href="freealg.html#K3" target="_self">DTConUA</a> <font color="Maroon">f</font>,<font color="Maroon">D</font></span>)</span></span>)</span> )
 
<b>by </b><i>, , <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a>, <a class="ref" href="unialg_2.html#T2">UNIALG_2:2</a></i>;<br/>
<b>hence </b><a NAME="E9:39"/>
 <a href="unialg_1.html#K3">arity</a> <font color="Maroon">o</font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i>, <a class="ref" href="pralg_1.html#T1">PRALG_1:1</a></i>;<br/>


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