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<span class="kw">let </span><font color="Maroon" title="c1">E</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">A</font> being  <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#K8" title="AFINSQ_1:func.8">^omega</a> </span>)</span><br/> for <font color="Olive" title="b2">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Olive" title="b1">A</font> <a href="flang_3.html#K1" title="FLANG_3:func.1">|^..</a> <font color="Olive" title="b2">n</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">A</font> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</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#K8" title="AFINSQ_1:func.8">^omega</a> </span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Maroon" title="c2">A</font> <a href="flang_3.html#K1" title="FLANG_3:func.1">|^..</a> <font color="Olive" title="b1">n</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A</font> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">A</font> <a href="flang_3.html#K1" title="FLANG_3:func.1">|^..</a> <font color="Maroon" title="c3">n</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A</font> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a> </span><br/>





<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">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="c3">n</font> implies <font color="Maroon" title="c4">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#K8" title="FLANG_1:func.8">*</a>  )</span><br/><span class="kw">assume </span><a NAME="E1:10_1"/>
<font color="Maroon" title="c4">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="c3">n</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">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#K8" title="FLANG_1:func.8">*</a> </span><br/><a NAME="E2:10_1"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <br/>( <font color="Maroon" title="c3">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font> &amp; <font color="Maroon" title="c4">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="Olive" title="b1">k</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="flang_3.html#T2" target="_self" title="FLANG_3:th.2">Th2</a></span>;<br/><span class="kw">hence </span><a NAME="E3:10_1"/>
<font color="Maroon" title="c4">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#K8" title="FLANG_1:func.8">*</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="flang_1.html#T42" title="FLANG_1:th.42">FLANG_1:42</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:10"/>
<font color="Maroon" title="c2">A</font> <a href="flang_3.html#K1" title="FLANG_3:func.1">|^..</a> <font color="Maroon" title="c3">n</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A</font> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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