<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E52">Th50</font></span>: <a NAME="T50"><span class="comment"><font color="firebrick">:: NUMBER13:50</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font>, <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">y</font>, <font color="Olive" title="b4">z</font>, <font color="Olive" title="b5">t</font> being   <a href="xxreal_0.html#V2" title="XXREAL_0:attr.2">positive</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds <br/> ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">n</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Olive" title="b2">x</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">n</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Olive" title="b3">y</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">n</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Olive" title="b4">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">n</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Olive" title="b5">t</font> iff ( ( <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Olive" title="b3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">x</font> &amp; <font color="Olive" title="b4">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">x</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 &amp; <font color="Olive" title="b5">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">x</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2 ) or ( <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Olive" title="b3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">x</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 &amp; <font color="Olive" title="b4">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">x</font> &amp; <font color="Olive" title="b5">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">x</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2 ) or ( <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Olive" title="b4">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">y</font> &amp; <font color="Olive" title="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">y</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 &amp; <font color="Olive" title="b5">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">y</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2 ) or ( <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp; <font color="Olive" title="b3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">x</font> &amp; <font color="Olive" title="b4">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">x</font> &amp; <font color="Olive" title="b5">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">x</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 ) ) )</div></div>
