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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E3">Th3</font></span>: <a NAME="T3"><span class="comment"><font color="firebrick">:: DIOPHAN1:3</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b2">r</font> is  <a href="irrat_1.html#NV1" title="IRRAT_1:NV.1">irrational</a>  holds <br/>( <span class="p1">(<span class="default"><a href="real_3.html#NK4" title="REAL_3:NK.4">rfs</a> <font color="Olive" title="b2">r</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_3.html#NK4" title="REAL_3:NK.4">rfs</a> <font color="Olive" title="b2">r</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> 1</span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_3.html#NK4" title="REAL_3:NK.4">rfs</a> <font color="Olive" title="b2">r</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> 2</span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_3.html#NK6" title="REAL_3:NK.6">scf</a> <font color="Olive" title="b2">r</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> 1</span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_3.html#NK4" title="REAL_3:NK.4">rfs</a> <font color="Olive" title="b2">r</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )</div></div>
