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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:1_1"/>
not <font color="Maroon">c<sub>1</sub></font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><a NAME="E2:1_1"/><b>then </b>
0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><a NAME="E3:1_1"/><b>then </b>
0 <a href="binop_2.html#K23">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><b>hence </b><a NAME="E4:1_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 )
 <b>by </b><i><a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 )
 ;<br/>

<a NAME="E3:1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
;<br/>
<b>hence </b><a NAME="E4:1"/>
not <font color="Maroon">c<sub>1</sub></font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/>


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