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<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:1_1_1_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">fss</font></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:1_1_1_1"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">fss</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">fss</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/><b>reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">n</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E6:1_1_1_1"/><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">fs</font> &amp; <font color="Maroon">x</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">fs</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> )
 <b>by </b><i>, <a class="ref" href="glib_001.html#T4">GLIB_001:4</a></i>;<br/><a NAME="E7:1_1_1_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">fs</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/><b>hence </b><a NAME="E8:1_1_1_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D</font>
 ;<br/></div><b>end;</b></div>
<a NAME="E2:1_1_1"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">fss</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">D</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<b>hence </b><a NAME="E3:1_1_1"/>
 <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">fss</font> is    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>


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