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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>assume </b><a NAME="E1:11"/><i><font color="Green">E9</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/>

<b>assume </b><a NAME="E2:11"/>
<font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K4">mod</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/>

<a NAME="E3:11"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="int_1.html#K6">mod</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="newton.html#T101">NEWTON:101</a></i>;<br/>
<a NAME="E4:11"/><b>then </b>
not <font color="Maroon">c<sub>1</sub></font> <a href="int_1.html#R2">divides</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="jordan1d.html#E1:11"><i><font color="Green">E9</font></i></a>, <a class="ref" href="int_3.html#T11">INT_3:11</a></i>;<br/>
<a NAME="E5:11"/><b>then </b><i><font color="Green">E10</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font> is  not   <a href="int_1.html#NM1">Integer</a>
 
<b>by </b><i><a class="txt" href="jordan1d.html#E1:11"><i><font color="Green">E9</font></i></a>, <a class="ref" href="wsierp_1.html#T22">WSIERP_1:22</a></i>;<br/>
<b>thus </b> <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K3">div</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> = 
 <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="int_1.html#K5">div</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T101">NEWTON:101</a></i>
<br/>.= 
 <a href="xcmplx_0.html#K4">-</a> <span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="int_1.html#K1">/]</a></span>
<b>by </b><i><a class="ref" href="int_1.html#D7">INT_1:def 7</a></i>
<br/>.= 
<span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="int_1.html#K1">/]</a></span> <a href="xcmplx_0.html#K2">+</a> 1
<b>by </b><i><a class="txt" href="jordan1d.html#E5:11"><i><font color="Green">E10</font></i></a>, <a class="ref" href="jordan1d.html#T3" target="_self">Th3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="int_1.html#K5">div</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
<b>by </b><i><a class="ref" href="int_1.html#D7">INT_1:def 7</a></i>
;<br/>


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