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<b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">j</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/>





<b>assume </b><a NAME="E1:23"/><i><font color="Green">E34</font></i>: 
( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">j</font> )
 ;<br/>

<b>then reconsider </b><font color="Maroon">X</font> = <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">i</font>,<font color="Maroon">x</font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">j</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K2">}</a></span> as   <a href="funct_1.html#NM1">Function</a> <b>by </b><i><a class="ref" href="grfunc_1.html#T19">GRFUNC_1:19</a></i>;<br/>
<a NAME="E3:23"/><i><font color="Green">E35</font></i>: 
0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font>
 
<b>by </b><i>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E4:23"/>
<font color="Maroon">X</font> is <a href="finseq_1.html#V2">FinSubsequence-like</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1"><b>proof </b></a><div class="add">

<a NAME="E1:23_1"/><i><font color="Green">E39</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">i</font>,<font color="Maroon">j</font></span><a href="domain_1.html#K7">}</a></span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T24">RELAT_1:24</a></i>;<br/>
<a NAME="E2:23_1"/>
<span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">i</font>,<font color="Maroon">j</font></span><a href="domain_1.html#K7">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">j</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:23_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">i</font>,<font color="Maroon">j</font></span><a href="domain_1.html#K7">}</a></span>
 ;<br/><a NAME="E2:23_1_1_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> )
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><b>hence </b><a NAME="E3:23_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">j</font>
 <b>by </b><i>, , <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a>, <a class="ref" href="finseq_1.html#T5">FINSEQ_1:5</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:23_1_1"/>
<span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">i</font>,<font color="Maroon">j</font></span><a href="domain_1.html#K7">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:23_1"/>
<font color="Maroon">X</font> is <a href="finseq_1.html#V2">FinSubsequence-like</a>
 <b>by </b><i>, <a class="ref" href="finseq_1.html#D12">FINSEQ_1:def 12</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:23"/>
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">i</font>,<font color="Maroon">x</font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">j</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K2">}</a></span> is   <a href="finseq_1.html#NM4">FinSubsequence</a>
 ;<br/>


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