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







<b>set </b><font color="Maroon">fd</font> =  <a href="real_3.html#K2" target="_self">divSeq</a> <font color="Maroon">m</font>,<font color="Maroon">n</font>;<br/>
<b>set </b><font color="Maroon">fm</font> =  <a href="real_3.html#K1" target="_self">modSeq</a> <font color="Maroon">m</font>,<font color="Maroon">n</font>;<br/>
<b>assume </b><a NAME="E1:35"/>
<font color="Maroon">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">b</font>
 ;<br/>

<a NAME="E2:35"/><b>then </b><i><font color="Green">E31</font></i>: 
<font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<b>assume </b><a NAME="E3:35"/>
<span class="p1">(<span class="default"><a href="real_3.html#K1" target="_self">modSeq</a> <font color="Maroon">m</font>,<font color="Maroon">n</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0
 ;<br/>

<a NAME="E4:35"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_3.html#K2" target="_self">divSeq</a> <font color="Maroon">m</font>,<font color="Maroon">n</font></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:35"/>
<span class="p1">(<span class="default"><a href="real_3.html#K2" target="_self">divSeq</a> <font color="Maroon">m</font>,<font color="Maroon">n</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i>, </i>;<br/>


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