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<span class="kw">let </span><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font> be   <a href="rat_1.html#NM1" title="RAT_1:NM.1">Rational</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">p</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c3">q</font> is   <a href="rat_1.html#NM1" title="RAT_1:NM.1">Rational</a></span><br/>



<span class="kw">consider </span><font color="Maroon" title="c4">m1</font>, <font color="Maroon" title="c5">n1</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><span class="kw"> such that </span><br/><a NAME="E2:34"/>
<font color="Maroon" title="c5">n1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">and </span><br/><a NAME="E3:34"/><span class="lab"><font color="Green" title="E14">A1</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">m1</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c5">n1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rat_1.html#T3" target="_self" title="RAT_1:th.3">Th3</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c6">m2</font>, <font color="Maroon" title="c7">n2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><span class="kw"> such that </span><br/><a NAME="E5:34"/>
<font color="Maroon" title="c7">n2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">and </span><br/><a NAME="E6:34"/><span class="lab"><font color="Green" title="E15">A2</font></span>: 
<font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">m2</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c7">n2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rat_1.html#T3" target="_self" title="RAT_1:th.3">Th3</a></span>;<br/>
<font color="Maroon" title="c2">p</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c3">q</font> = 
<font color="Maroon" title="c2">p</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">m2</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c7">n2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:34"><span class="lab"><font color="Green" title="E15">A2</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c2">p</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c7">n2</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c6">m2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_1.html#T78" title="XCMPLX_1:th.78">XCMPLX_1:78</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">m1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c7">n2</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">n1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c6">m2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:34"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="ref" href="xcmplx_1.html#T77" title="XCMPLX_1:th.77">XCMPLX_1:77</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E8:34"/>
<font color="Maroon" title="c2">p</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c3">q</font> is   <a href="rat_1.html#NM1" title="RAT_1:NM.1">Rational</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rat_1.html#T6" target="_self" title="RAT_1:th.6">Th6</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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