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<b>let </b><font color="Maroon">p</font> be   <a href="rat_1.html#NM1">Rational</a>;<br/>

<a NAME="E1:45"/><i><font color="Green">E28</font></i>: 
0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rat_1.html#K1" target="_self">denominator</a> <font color="Maroon">p</font>
 
<b>by </b><i/>;<br/>
<div><i><font color="Green">E29</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="45_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:45_1"/>
 <a href="rat_1.html#K2" target="_self">numerator</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="rat_1.html#K1" target="_self">denominator</a> <font color="Maroon">p</font></span>)</span>
 ;<br/><b>hence </b><font color="Maroon">p</font> = 
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><a href="rat_1.html#K1" target="_self">denominator</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><a href="rat_1.html#K1" target="_self">denominator</a> <font color="Maroon">p</font></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rat_1.html#K1" target="_self">denominator</a> <font color="Maroon">p</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><a href="rat_1.html#K1" target="_self">denominator</a> <font color="Maroon">p</font></span>)</span></span>)</span>

<br/>.= 
 <a href="real_1.html#K1">-</a> 1
<b>by </b><i><a class="txt" href="rat_1.html#E1:45"><i><font color="Green">E28</font></i></a>, <a class="ref" href="xcmplx_1.html#T60">XCMPLX_1:60</a></i>
;<br/><br/></div><b>end;</b></div>
<b>thus </b><a NAME="E3:45"/>
(  <a href="rat_1.html#K2" target="_self">numerator</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="rat_1.html#K1" target="_self">denominator</a> <font color="Maroon">p</font></span>)</span> iff <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1 )
 <b>by </b><i><a class="txt" href="rat_1.html#E2:45"><i><font color="Green">E29</font></i></a></i>;<br/>


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