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<a NAME="E1:4"/>
(  <a href="power.html#K4" title="POWER:func.4">number_e</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  &amp;  not  <a href="power.html#K4" title="POWER:func.4">number_e</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K3" title="NUMBERS:func.3">RAT</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_0.html#D1" onmouseover="rs('xreal_0/D1')" onmouseout="rh()">XREAL_0:def 1</a></span>;<br/>
<a NAME="E2:4"/><span class="kw">then </span>
 <a href="power.html#K4" title="POWER:func.4">number_e</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <a href="numbers.html#K3" title="NUMBERS:func.3">RAT</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D5" onmouseover="rs('xboole_0/D5')" onmouseout="rh()">XBOOLE_0:def 5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:4"/>
 <a href="power.html#K4" title="POWER:func.4">number_e</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="numbers.html#T18" onmouseover="rs('numbers/T18')" onmouseout="rh()">NUMBERS:18</a>, <a class="ref" href="xboole_1.html#T34" onmouseover="rs('xboole_1/T34')" onmouseout="rh()">XBOOLE_1:34</a>, <a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</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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