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<b>let </b><font color="Maroon">i</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">j</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>assume </b><a NAME="E1:35"/>
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">i</font>
 ;<br/>

<a NAME="E2:35"/><b>then </b>
 ex <font color="Olive">k</font> being  <a href="nat_1.html#NM1">Nat</a> st <br/>( <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="xcmplx_0.html#K3">*</a> <font color="Olive">k</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="nat_1.html#K6" target="_self">mod</a> <font color="Maroon">i</font></span>)</span> &amp; <font color="Maroon">j</font> <a href="nat_1.html#K6" target="_self">mod</a> <font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">i</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:35"/>
<font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">j</font> <a href="nat_1.html#K5" target="_self">div</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="nat_1.html#K6" target="_self">mod</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i/>;<br/>


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