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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="int_1.html#NM1">Integer</a>;<br/>

<b>assume </b><a NAME="E1:9"/>
<font color="Maroon">c<sub>1</sub></font> is   <a href="nat_1.html#NM1">Nat</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>2</sub></font> = <font color="Maroon">c<sub>1</sub></font> as   <a href="nat_1.html#NM1">Nat</a> ;<br/>
<a NAME="E3:9"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</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>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span><a href="int_1.html#K1">/]</a></span> )
 
<b>by </b><i><a class="ref" href="int_1.html#D4">INT_1:def 4</a></i>;<br/>
<a NAME="E4:9"/><b>then </b>
( <font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 2 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="xcmplx_0.html#K7">/</a> 2 &amp; 0 <a href="xcmplx_0.html#K7">/</a> 2 <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</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>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</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="ref" href="real_1.html#T73">REAL_1:73</a>, <a class="ref" href="xreal_1.html#T21">XREAL_1:21</a></i>;<br/>
<a NAME="E5:9"/><b>then </b>
<span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span><a href="int_1.html#K1">/]</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="ref" href="int_1.html#T20">INT_1:20</a></i>;<br/>
<a NAME="E6:9"/><b>then </b>
<span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span><a href="int_1.html#K1">/]</a></span> is   <a href="nat_1.html#NM1">Nat</a>
 
<b>by </b><i><a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/>
<b>hence </b><a NAME="E7:9"/>
<font color="Maroon">c<sub>1</sub></font> <a href="int_1.html#K5">div</a> 2 is   <a href="nat_1.html#NM1">Nat</a>
 <b>by </b><i><a class="ref" href="int_1.html#D7">INT_1:def 7</a></i>;<br/>


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