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<b>let </b><font color="Maroon" title="c1">E</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">B</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="afinsq_1.html#K10" title="AFINSQ_1:func.10">^omega</a> </span>)</span>;<br/><b>let </b><font color="Maroon" title="c4">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>







<b>assume </b><a NAME="E1:14"/><i><font color="Green" title="E11">A1</font></i>: 
<font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">B</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:14_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> <a href="flang_3.html#K1" title="FLANG_3:func.1">|^..</a> <font color="Maroon" title="c4">n</font>
 ;<br/><b>then consider </b><font color="Maroon" title="c6">k</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E3:14_1"/><i><font color="Green" title="E12">A2</font></i>: 
( <font color="Maroon" title="c4">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font> &amp; <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Maroon" title="c6">k</font> )
 <b>by </b><i><a class="ref" href="flang_3.html#T2" target="_self" title="FLANG_3:th.2">Th2</a></i>;<br/><a NAME="E4:14_1"/>
<font color="Maroon" title="c2">A</font> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Maroon" title="c6">k</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">B</font> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Maroon" title="c6">k</font>
 <b>by </b><i><a class="txt" href="flang_3.html#E1:14"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="flang_1.html#T38" title="FLANG_1:th.38">FLANG_1:38</a></i>;<br/><b>hence </b><a NAME="E5:14_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> <a href="flang_3.html#K1" title="FLANG_3:func.1">|^..</a> <font color="Maroon" title="c4">n</font>
 <b>by </b><i><a class="txt" href="flang_3.html#E3:14_1"><i><font color="Green" title="E12">A2</font></i></a>, <a class="ref" href="flang_3.html#T2" target="_self" title="FLANG_3:th.2">Th2</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:14"/>
<font color="Maroon" title="c2">A</font> <a href="flang_3.html#K1" title="FLANG_3:func.1">|^..</a> <font color="Maroon" title="c4">n</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">B</font> <a href="flang_3.html#K1" title="FLANG_3:func.1">|^..</a> <font color="Maroon" title="c4">n</font>
 <b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>


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