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<div><span class="kw">theorem </span><a NAME="T52"><span class="comment"><font color="firebrick">:: NUMBER15:52</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font>, <font color="Olive" title="b4">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>  st <font color="Olive" title="b1">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">y</font> &amp; <font color="Olive" title="b2">y</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b3">z</font> &amp; <font color="Olive" title="b3">z</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b4">t</font> holds <br/>( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Olive" title="b2">y</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Olive" title="b3">z</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Olive" title="b4">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 iff ( ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp; <font color="Olive" title="b3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 &amp; <font color="Olive" title="b4">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 42 ) or ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp; <font color="Olive" title="b3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 &amp; <font color="Olive" title="b4">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 24 ) or ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp; <font color="Olive" title="b3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9 &amp; <font color="Olive" title="b4">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 18 ) or ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp; <font color="Olive" title="b3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10 &amp; <font color="Olive" title="b4">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 15 ) or ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp; <font color="Olive" title="b3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 &amp; <font color="Olive" title="b4">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 ) or ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 &amp; <font color="Olive" title="b3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 &amp; <font color="Olive" title="b4">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 20 ) or ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 &amp; <font color="Olive" title="b3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 &amp; <font color="Olive" title="b4">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 ) or ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 &amp; <font color="Olive" title="b3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 &amp; <font color="Olive" title="b4">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 ) or ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 &amp; <font color="Olive" title="b3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 &amp; <font color="Olive" title="b4">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10 ) or ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 &amp; <font color="Olive" title="b3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 &amp; <font color="Olive" title="b4">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 ) or ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp; <font color="Olive" title="b3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 &amp; <font color="Olive" title="b4">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 ) or ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp; <font color="Olive" title="b3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 &amp; <font color="Olive" title="b4">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 ) or ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 &amp; <font color="Olive" title="b3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 &amp; <font color="Olive" title="b4">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 ) or ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 &amp; <font color="Olive" title="b3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 &amp; <font color="Olive" title="b4">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 ) ) )</div></div>
