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<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/>

<div><i><font color="Green">E32</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="61_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:61_1"/>
<font color="Maroon">c<sub>1</sub></font> is   <a href="int_1.html#NM1">Integer</a>
 ;<br/><b>hence </b><a NAME="E2:61_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> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="int_1.html#K2" target="_self">[/</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="int_1.html#K2" target="_self">\]</a></span> )
 <b>by </b><i><a class="ref" href="int_1.html#T47" target="_self">Th47</a>, <a class="ref" href="int_1.html#T54" target="_self">Th54</a></i>;<br/><b>hence </b><a NAME="E3:61_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> <span class="p1"><a href="int_1.html#K2" target="_self">[/</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="int_1.html#K2" target="_self">\]</a></span>
 ;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:61_2"/>
<font color="Maroon">c<sub>1</sub></font> is  not   <a href="int_1.html#NM1">Integer</a>
 ;<br/><a NAME="E2:61_2"/><b>then </b>
( <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="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1"><a href="int_1.html#K2" target="_self">[/</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="int_1.html#K2" target="_self">\]</a></span> )
 <b>by </b><i><a class="ref" href="int_1.html#T48" target="_self">Th48</a>, <a class="ref" href="int_1.html#T55" target="_self">Th55</a></i>;<br/><b>hence </b><a NAME="E3:61_2"/>
<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#NR2" target="_self">&lt;&gt;</a> <span class="p1"><a href="int_1.html#K2" target="_self">[/</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="int_1.html#K2" target="_self">\]</a></span>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:61"/>
( <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> <span class="p1"><a href="int_1.html#K2" target="_self">[/</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="int_1.html#K2" target="_self">\]</a></span> iff <font color="Maroon">c<sub>1</sub></font> is <a href="int_1.html#V1" target="_self">integer</a> )
 <b>by </b><i><a class="txt" href="int_1.html#E1:61"><i><font color="Green">E32</font></i></a></i>;<br/>


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