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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="counters.html#V2" title="COUNTERS:attr.2">ext-natural-membered</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">N</font> being   <a href="counters.html#NM1" title="COUNTERS:NM.1">ExtNat</a> st <font color="Olive" title="b1">N</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c2">x</font> being   <a href="xxreal_0.html#NM1" title="XXREAL_0:NM.1">ExtReal</a><span class="kw"> such that </span><br/><a NAME="E2:33"/><span class="lab"><font color="Green" title="E10">A1</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="membered.html#T8" onmouseover="rs('membered/T8')" onmouseout="rh()">MEMBERED:8</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c3">N</font> = <font color="Maroon" title="c2">x</font> as   <a href="counters.html#V1" title="COUNTERS:attr.1">ext-natural</a>  <a href="xxreal_0.html#NM1" title="XXREAL_0:NM.1">ExtReal</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:33"><span class="lab"><font color="Green" title="E10">A1</font></span></a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c3">N</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">N</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font></span><br/>

<span class="kw">thus </span><a NAME="E4:33"/>
<font color="Maroon" title="c3">N</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:33"><span class="lab"><font color="Green" title="E10">A1</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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