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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="rat_1.html#NM1">Rational</a>;<br/>





<b>assume </b><a NAME="E1:65"/><i><font color="Green">E51</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<a NAME="E2:65"/><b>then </b><i><font color="Green">E52</font></i>: 
(  <a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 1 &amp;  <a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="rat_1.html#T40">RAT_1:40</a></i>;<br/>
<a NAME="E3:65"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p1">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="txt" href="prepower.html#E1:65"><i><font color="Green">E51</font></i></a>, <a class="ref" href="prepower.html#T49" target="_self">Th49</a></i>;<br/>
<b>thus </b><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K8" target="_self">#Q</a> <font color="Maroon">c<sub>3</sub></font> = 
1 <a href="prepower.html#K4" target="_self">-Root</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p2">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="prepower.html#E2:65"><i><font color="Green">E52</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p1">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="prepower.html#E3:65"><i><font color="Green">E53</font></i></a>, <a class="ref" href="prepower.html#T30" target="_self">Th30</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default"><a href="prepower.html#K1" target="_self">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="prepower.html#E2:65"><i><font color="Green">E52</font></i></a>, <a class="ref" href="prepower.html#D4" target="_self">Def4</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="newton.html#K2">|^</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>
;<br/>


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