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<b>let </b><font color="Maroon" title="c2">p</font> be   <a href="rat_1.html#NM1" title="RAT_1:NM.1">Rational</a>;<br/>

<a NAME="E1:58"/><i><font color="Green" title="E37">A1</font></i>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="rat_1.html#K1" title="RAT_1:func.1">denominator</a> <font color="Maroon" title="c2">p</font>
 
<b>by </b><i><a class="ref" href="rat_1.html#T27" target="_self" title="RAT_1:th.27">Th27</a></i>;<br/>
<a NAME="E2:58"/><i><font color="Green" title="E38">A2</font></i>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="rat_1.html#K1" title="RAT_1:func.1">denominator</a> <font color="Maroon" title="c2">p</font>
 
<b>by </b><i><a class="ref" href="rat_1.html#D3" target="_self" title="RAT_1:def.3">Def3</a></i>;<br/>
<a NAME="E3:58"/><i><font color="Green" title="E39">A3</font></i>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="rat_1.html#K1" title="RAT_1:func.1">denominator</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> 
 
<b>by </b><i><a class="ref" href="rat_1.html#T30" target="_self" title="RAT_1:th.30">Th30</a></i>;<br/>
<div><i><font color="Green" title="E40">A4</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:58_1"/>
<font color="Maroon" title="c2">p</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><a NAME="E2:58_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="rat_1.html#K2" title="RAT_1:func.2">numerator</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><a href="rat_1.html#K1" title="RAT_1:func.1">denominator</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="rat_1.html#T37" target="_self" title="RAT_1:th.37">Th37</a></i>;<br/><a NAME="E3:58_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rat_1.html#K2" title="RAT_1:func.2">numerator</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><a href="rat_1.html#K1" title="RAT_1:func.1">denominator</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><a href="rat_1.html#K1" title="RAT_1:func.1">denominator</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p1">(<span class="default"><a href="rat_1.html#K1" title="RAT_1:func.1">denominator</a> <font color="Maroon" title="c2">p</font></span>)</span>
 <b>by </b><i><a class="txt" href="rat_1.html#E1:58"><i><font color="Green" title="E37">A1</font></i></a>, <a class="ref" href="xreal_1.html#T70" title="XREAL_1:th.70">XREAL_1:70</a></i>;<br/><b>hence </b><a NAME="E4:58_1"/>
 <a href="rat_1.html#K2" title="RAT_1:func.2">numerator</a> <font color="Maroon" title="c2">p</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="rat_1.html#E2:58"><i><font color="Green" title="E38">A2</font></i></a>, <a class="ref" href="xcmplx_1.html#T88" title="XCMPLX_1:th.88">XCMPLX_1:88</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:58_2"/>
 <a href="rat_1.html#K2" title="RAT_1:func.2">numerator</a> <font color="Maroon" title="c2">p</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><a NAME="E2:58_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="rat_1.html#K2" title="RAT_1:func.2">numerator</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rat_1.html#K1" title="RAT_1:func.1">denominator</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rat_1.html#K1" title="RAT_1:func.1">denominator</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span>
 <b>by </b><i><a class="txt" href="rat_1.html#E3:58"><i><font color="Green" title="E39">A3</font></i></a>, <a class="ref" href="xreal_1.html#T70" title="XREAL_1:th.70">XREAL_1:70</a></i>;<br/><b>hence </b><a NAME="E3:58_2"/>
<font color="Maroon" title="c2">p</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="rat_1.html#T37" target="_self" title="RAT_1:th.37">Th37</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:58"/>
( <font color="Maroon" title="c2">p</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  iff  <a href="rat_1.html#K2" title="RAT_1:func.2">numerator</a> <font color="Maroon" title="c2">p</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <b>by </b><i><a class="txt" href="rat_1.html#E4:58"><i><font color="Green" title="E40">A4</font></i></a></i>;<br/>


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