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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">m</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">l</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:123"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">n</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">m</font> &amp; <font color="Maroon">n</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">l</font> )
 ;<br/>

<a NAME="E2:123"/><b>then </b><i><font color="Green">E32</font></i>: 
<font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K5">div</a> <font color="Maroon">n</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">E34</font></i>:  <a href="real_1.html#K1">-</a> <font color="Maroon">l</font> = 
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><font color="Maroon">l</font> <a href="nat_1.html#K5">div</a> <font color="Maroon">n</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="nat_1.html#T49">NAT_1:49</a></i>
<br/>.= 
<font color="Maroon">n</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">l</font> <a href="nat_1.html#K5">div</a> <font color="Maroon">n</font></span>)</span></span>)</span>

;<br/>
<a NAME="E4:123"/>
<font color="Maroon">m</font> <a href="real_1.html#K5">-</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K5">div</a> <font color="Maroon">n</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">l</font> <a href="nat_1.html#K5">div</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E5:123"/>
<font color="Maroon">n</font> <a href="int_1.html#R2">divides</a> <font color="Maroon">m</font> <a href="real_1.html#K5">-</a> <font color="Maroon">l</font>
 <b>by </b><i><a class="ref" href="int_1.html#D9">INT_1:def 9</a></i>;<br/>


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