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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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="rat_1.html#V1" title="RAT_1:attr.1">irrational</a></span><br/>

<a NAME="E1:36"/>
 <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>
 
<b>by </b><i><a class="ref" href="int_1.html#D6" title="INT_1:def.6">INT_1:def 6</a></i>;<br/>
<b>hence </b><a NAME="E2:36"/>
 <a href="int_1.html#K4" title="INT_1:func.4">frac</a> <font color="Maroon" title="c1">r</font> is <a href="rat_1.html#V1" title="RAT_1:attr.1">irrational</a>
 <b>by </b><i><a class="ref" href="borsuk_5.html#T41" target="_self" title="BORSUK_5:th.41">Th41</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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