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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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">p</font> is   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> implies (  <a href="rat_1.html#K1" title="RAT_1:func.1">denominator</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp;  <a href="rat_1.html#K2" title="RAT_1:func.2">numerator</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> ) )</span><br/>

<b>assume </b><a NAME="E1:39"/>
<font color="Maroon" title="c2">p</font> is   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="rat_1.html#K1" title="RAT_1:func.1">denominator</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp;  <a href="rat_1.html#K2" title="RAT_1:func.2">numerator</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> )</span><br/>

<b>then reconsider </b><font color="Maroon" title="c3">m</font> = <font color="Maroon" title="c2">p</font> as   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> ;<br/>
<a NAME="E3:39"/>
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">m</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 1
 
;<br/>
<a NAME="E4:39"/><b>then </b><i><font color="Green" title="E25">A1</font></i>: 
 <a href="rat_1.html#K1" title="RAT_1:func.1">denominator</a> <font color="Maroon" title="c2">p</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1
 
<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="E5:39"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&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#T29" target="_self" title="RAT_1:th.29">Th29</a></i>;<br/>
<b>hence </b><a NAME="E6:39"/>
 <a href="rat_1.html#K1" title="RAT_1:func.1">denominator</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>by </b><i><a class="txt" href="rat_1.html#E4:39"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="rat_1.html#K2" title="RAT_1:func.2">numerator</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font></span><br/>

<b>hence </b><a NAME="E7:39"/>
 <a href="rat_1.html#K2" title="RAT_1:func.2">numerator</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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