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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1">Nat</a>,   <a href="hidden.html#M1">set</a> ] <b>means </b>for <font color="Olive">h</font> being non <a href="xboole_0.html#V1">empty</a> <a href="unialg_1.html#V1" target="_self">homogeneous</a> <a href="partfun1.html#NM1">PartFunc</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font> <a href="finseq_1.html#K13">*</a> ,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font>  st <font color="Olive">h</font> <a href="hidden.html#R1">=</a> the <a href="unialg_1.html#U1" target="_self">charact</a> of <font color="Maroon">U1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a<sub>1</sub></font> holds <br/><font color="Maroon">a<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="unialg_1.html#K3" target="_self">arity</a> <font color="Olive">h</font>;<br/>
<div><i><font color="Green">E28</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:24_1_1_1"/>
<font color="Maroon">m</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> the <a href="unialg_1.html#U1" target="_self">charact</a> of <font color="Maroon">U1</font></span>)</span>
 ;<br/><a NAME="E2:24_1_1_1"/><b>then </b>
<font color="Maroon">m</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> the <a href="unialg_1.html#U1" target="_self">charact</a> of <font color="Maroon">U1</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><b>then reconsider </b><font color="Maroon">H</font> = the <a href="unialg_1.html#U1" target="_self">charact</a> of <font color="Maroon">U1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">m</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="unialg_1.html#V1" target="_self">homogeneous</a> <a href="partfun1.html#NM1">PartFunc</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font> <a href="finseq_1.html#K13">*</a> ,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font> <b>by </b><i>, , <a class="ref" href="funct_1.html#D15">FUNCT_1:def 15</a></i>;<br/><b>reconsider </b><font color="Maroon">n</font> =  <a href="unialg_1.html#K3" target="_self">arity</a> <font color="Maroon">H</font> as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  ;<br/><b>take </b><font color="Maroon">n</font> = <font color="Maroon">n</font>;<br/><b>thus </b><a NAME="E5:24_1_1_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">m</font>,<font color="Maroon">n</font>]
 ;<br/></div><b>end;</b></div>
<b>consider </b><font color="Maroon">p</font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:24_1_1"/><i><font color="Green">E29</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</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> the <a href="unialg_1.html#U1" target="_self">charact</a> of <font color="Maroon">U1</font></span>)</span>
 <b>and </b><br/><a NAME="E4:24_1_1"/><i><font color="Green">E30</font></i>: 
for <font color="Olive">m</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">m</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> the <a href="unialg_1.html#U1" target="_self">charact</a> of <font color="Maroon">U1</font></span>)</span> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">m</font>,<font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Olive">m</font>]
 <b>from </b><i><a class="ref" href="finseq_1.html#S5">FINSEQ_1:sch 5</a>();<br/></i>
<b>take </b>
<font color="Maroon">p</font>
;<br/>

<b>thus </b><a NAME="E5:24_1_1"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> the <a href="unialg_1.html#U1" target="_self">charact</a> of <font color="Maroon">U1</font>
 <b>by </b><i>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>

<b>let </b><font color="Maroon">n</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E6:24_1_1"/><i><font color="Green">E31</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">p</font>
 ;<br/>

<b>let </b><font color="Maroon">h</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="unialg_1.html#V1" target="_self">homogeneous</a> <a href="partfun1.html#NM1">PartFunc</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font> <a href="finseq_1.html#K13">*</a> ,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font>;<br/>

<b>assume </b><a NAME="E7:24_1_1"/>
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a> the <a href="unialg_1.html#U1" target="_self">charact</a> of <font color="Maroon">U1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
 ;<br/>

<b>hence </b><a NAME="E8:24_1_1"/>
<font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a>  <a href="unialg_1.html#K3" target="_self">arity</a> <font color="Maroon">h</font>
 <b>by </b><i>, , </i>;<br/>


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