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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E33">Th42</font></span>: <a NAME="T30"><span class="comment"><font color="firebrick">:: DIOPHAN2:30</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">r</font> being   <a href="irrat_1.html#NV1" title="IRRAT_1:NV.1">irrational</a>  <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b2">r1</font> being   non  <a href="xxreal_0.html#V3" title="XXREAL_0:attr.3">negative</a>  <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  ex <font color="Olive" title="b3">q</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K3" title="NUMBERS:func.3">RAT</a>  st <br/>(  <a href="rat_1.html#K1" title="RAT_1:func.1">denominator</a> <font color="Olive" title="b3">q</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <span class="p1"><a href="int_1.html#K1" title="INT_1:func.1">[\</a><span class="default"><font color="Olive" title="b2">r1</font></span><a href="int_1.html#K1" title="INT_1:func.1">/]</a></span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 &amp; <font color="Olive" title="b3">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="diophan2.html#K2" title="DIOPHAN2:func.2">HWZSet</a> <font color="Olive" title="b1">r</font> )</div></div>
