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<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<a NAME="E1:51"/>
( <font color="Maroon">c<sub>1</sub></font> is   <a href="int_1.html#NM1">Integer</a> implies <span class="p1"><a href="int_1.html#K1" target="_self">[\</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="int_1.html#K1" target="_self">/]</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_1"><b>proof </b></a><div class="add">

<a NAME="E1:51_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K2">+</a> 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K2">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E2:51_1"/><b>then </b><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K6">-</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<b>assume </b><a NAME="E3:51_1"/>
<font color="Maroon">c<sub>1</sub></font> is   <a href="int_1.html#NM1">Integer</a>
 ;<br/>

<b>hence </b><a NAME="E4:51_1"/>
<span class="p1"><a href="int_1.html#K1" target="_self">[\</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="int_1.html#K1" target="_self">/]</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="int_1.html#E2:51_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="int_1.html#D4" target="_self">Def4</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:51"/>
( <span class="p1"><a href="int_1.html#K1" target="_self">[\</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="int_1.html#K1" target="_self">/]</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> iff <font color="Maroon">c<sub>1</sub></font> is <a href="int_1.html#V1" target="_self">integer</a> )
 ;<br/>


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