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<a NAME="E1:83"/>
<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <a href="borsuk_5.html#K1" title="BORSUK_5:func.1">IRRAT</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <a href="numbers.html#K3" title="NUMBERS:func.3">RAT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_5.html#D3" title="BORSUK_5:def.3">BORSUK_5:def 3</a>, <a class="ref" href="xboole_1.html#T48" title="XBOOLE_1:th.48">XBOOLE_1:48</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:83"/>
 <a href="numbers.html#K3" title="NUMBERS:func.3">RAT</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <a href="borsuk_5.html#K1" title="BORSUK_5:func.1">IRRAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="numbers.html#T12" title="NUMBERS:th.12">NUMBERS:12</a>, <a class="ref" href="xboole_1.html#T28" title="XBOOLE_1:th.28">XBOOLE_1:28</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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