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<b>consider </b><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><b> such that </b><br/><a NAME="E2:17_2_1"/><i><font color="Green" title="E13">A3</font></i>: 
<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> 
 <b>and </b><br/><a NAME="E3:17_2_1"/><i><font color="Green" title="E14">A4</font></i>: 
<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>
 <b>by </b><i><a class="ref" href="rat_1.html#T3" target="_self" title="RAT_1:th.3">Th3</a></i>;<br/>
<b>consider </b><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><b> such that </b><br/><a NAME="E5:17_2_1"/><i><font color="Green" title="E15">A5</font></i>: 
<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> 
 <b>and </b><br/><a NAME="E6:17_2_1"/><i><font color="Green" title="E16">A6</font></i>: 
<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>
 <b>by </b><i><a class="ref" href="rat_1.html#T3" target="_self" title="RAT_1:th.3">Th3</a></i>;<br/>
<a NAME="E7:17_2_1"/>
<font color="Maroon" title="c2">p</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<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#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">m2</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c5">n1</font></span>)</span></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="c7">n2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E2:17_2_1"><i><font color="Green" title="E13">A3</font></i></a>, <a class="txt" href="#E3:17_2_1"><i><font color="Green" title="E14">A4</font></i></a>, <a class="txt" href="#E5:17_2_1"><i><font color="Green" title="E15">A5</font></i></a>, <a class="txt" href="#E6:17_2_1"><i><font color="Green" title="E16">A6</font></i></a>, <a class="ref" href="xcmplx_1.html#T117" title="XCMPLX_1:th.117">XCMPLX_1:117</a></i>;<br/>
<b>hence </b><a NAME="E8:17_2_1"/>
<font color="Maroon" title="c2">p</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">q</font> is <a href="rat_1.html#V1" title="RAT_1:attr.1">rational</a>
 <b>by </b><i><a class="ref" href="rat_1.html#T6" target="_self" title="RAT_1:th.6">Th6</a></i>; <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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