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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:124"/><i><font color="Green">E99</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<a NAME="E2:124"/><b>then </b><i><font color="Green">E100</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K2">*</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>
 
<b>by </b><i><a class="ref" href="nat_1.html#T49">NAT_1:49</a></i>;<br/>
<i><font color="Green">E101</font></i>:  <a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>3</sub></font> = 
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K3">div</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="prepower.html#E1:124"><i><font color="Green">E99</font></i></a>, <a class="ref" href="nat_1.html#T49">NAT_1:49</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K3">div</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>

;<br/>
<font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>3</sub></font> = 
<font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>

<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<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="real_1.html#K3">+</a> <span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K3">div</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="prepower.html#E2:124"><i><font color="Green">E100</font></i></a>, <a class="txt" href="prepower.html#E3:124"><i><font color="Green">E101</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E5:124"/>
<font color="Maroon">c<sub>1</sub></font> <a href="int_1.html#R2">divides</a> <font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="int_1.html#D9">INT_1:def 9</a></i>;<br/>


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