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<span class="kw">let </span><font color="Maroon" title="c1">r</font> be   <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>   <a href="irrat_1.html#NV1" title="IRRAT_1:NV.1">irrational</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="int_1.html#K4" title="INT_1:func.4">frac</a> <font color="Maroon" title="c1">r</font> is  <a href="irrat_1.html#NV1" title="IRRAT_1:NV.1">irrational</a> </span><br/>

<a NAME="E1:56"/>
 <a href="int_1.html#K4" title="INT_1:func.4">frac</a> <font color="Maroon" title="c1">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">r</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1"><a href="int_1.html#K1" title="INT_1:func.1">[\</a><span class="default"><font color="Maroon" title="c1">r</font></span><a href="int_1.html#K1" title="INT_1:func.1">/]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#D6" title="INT_1:def.6">INT_1:def 6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:56"/>
 <a href="int_1.html#K4" title="INT_1:func.4">frac</a> <font color="Maroon" title="c1">r</font> is  <a href="irrat_1.html#NV1" title="IRRAT_1:NV.1">irrational</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_5.html#T41" target="_self" title="BORSUK_5:th.41">Th41</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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