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<b>let </b><font color="Maroon" title="c1">k</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">i</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>;<br/>



<b>assume </b><a NAME="E1:78"/>
<font color="Maroon" title="c1">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">i</font>
 ;<br/>

<a NAME="E2:78"/><b>then </b><i><font color="Green" title="E37">A1</font></i>: 
<font color="Maroon" title="c1">k</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c1">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">k</font>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T11" title="XREAL_1:th.11">XREAL_1:11</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c3">j</font> = <font color="Maroon" title="c2">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">k</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="ref" href="int_1.html#T16" target="_self" title="INT_1:th.16">Th16</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c3">j</font>
;<br/>

<b>thus </b><a NAME="E4:78"/>
<font color="Maroon" title="c3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">k</font>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c4">j'</font> = <font color="Maroon" title="c3">j</font>, <font color="Maroon" title="c5">0'</font> = 0 as   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> ;<br/>
<a NAME="E6:78"/>
<font color="Maroon" title="c5">0'</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">j'</font>
 
<b>by </b><i><a class="txt" href="int_1.html#E2:78"><i><font color="Green" title="E37">A1</font></i></a>, <a class="ref" href="int_1.html#T20" target="_self" title="INT_1:th.20">Th20</a></i>;<br/>
<b>hence </b><a NAME="E7:78"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">j</font>
 ;<br/>


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