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



<a NAME="E1:60"/><i><font color="Green">E28</font></i>: 
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="rat_1.html#K1" target="_self">denominator</a> <font color="Maroon">p</font>
 
<b>by </b><i/>;<br/>
<a NAME="E2:60"/><i><font color="Green">E29</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/>
<a NAME="E3:60"/><i><font color="Green">E34</font></i>: 
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<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#K2">"</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E4:60"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">p</font> implies <font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="rat_1.html#K1" target="_self">denominator</a> <font color="Maroon">p</font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="rat_1.html#K2" target="_self">numerator</a> <font color="Maroon">p</font> )
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T70">XREAL_1:70</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:60_1"/>
<font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="rat_1.html#K1" target="_self">denominator</a> <font color="Maroon">p</font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="rat_1.html#K2" target="_self">numerator</a> <font color="Maroon">p</font>
 ;<br/><a NAME="E2:60_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</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="xcmplx_0.html#K3">*</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#K2">"</a> </span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="rat_1.html#K2" target="_self">numerator</a> <font color="Maroon">p</font></span>)</span> <a href="xcmplx_0.html#K3">*</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#K2">"</a> </span>)</span>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T70">XREAL_1:70</a></i>;<br/><a NAME="E3:60_1"/><b>then </b>
<font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</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#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<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#K2">"</a> </span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="rat_1.html#K2" target="_self">numerator</a> <font color="Maroon">p</font></span>)</span> <a href="xcmplx_0.html#K3">*</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#K2">"</a> </span>)</span>
 ;<br/><a NAME="E4:60_1"/><b>then </b>
<font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="rat_1.html#K2" target="_self">numerator</a> <font color="Maroon">p</font></span>)</span> <a href="xcmplx_0.html#K3">*</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#K2">"</a> </span>)</span>
 <b>by </b><i>, <a class="ref" href="xcmplx_0.html#D7">XCMPLX_0:def 7</a></i>;<br/><b>hence </b><a NAME="E5:60_1"/>
<font color="Maroon">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">p</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:60"/>
( <font color="Maroon">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">p</font> iff <font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="rat_1.html#K1" target="_self">denominator</a> <font color="Maroon">p</font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="rat_1.html#K2" target="_self">numerator</a> <font color="Maroon">p</font> )
 <b>by </b><i/>;<br/>


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