<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E23">Th19</font></span>: <a NAME="T19"><span class="comment"><font color="firebrick">:: IRRAT_1:19</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">k</font>, <font color="Olive" title="b2">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">x</font>, <font color="Olive" title="b4">y</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">n</font> holds <br/><span class="p1">(<span class="default">(<font color="Olive" title="b3">x</font>,<font color="Olive" title="b4">y</font>) <a href="newton.html#K5" title="NEWTON:func.5">In_Power</a> <font color="Olive" title="b2">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">n</font> <a href="newton.html#K4" title="NEWTON:func.4">choose</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">x</font> <a href="irrat_1.html#NK1" title="IRRAT_1:NK.1">^</a> <span class="p3">(<span class="default"><font color="Olive" title="b2">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Olive" title="b1">k</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">y</font> <a href="irrat_1.html#NK1" title="IRRAT_1:NK.1">^</a> <font color="Olive" title="b1">k</font></span>)</span></div></div>
