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

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="59_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:59_1"/>
( <font color="Maroon">j</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 or <font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="59_1_1"><b>suppose </b></a><a NAME="E1:59_1_1"/>
<font color="Maroon">j</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:59_1_1"/>
( <font color="Maroon">j</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 or <font color="Maroon">j</font> <a href="hidden.html#R1">=</a>  <a href="binop_2.html#K7">-</a> 1 or <font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;</a>  <a href="binop_2.html#K7">-</a> 1 )
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="59_1_2"><b>suppose </b></a><a NAME="E1:59_1_2"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;</a> 0
 ;<br/><div class="add"><a NAME="E2:59_1_2"/><b>then </b>
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">j</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="binop_2.html#K7">-</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/><b>then reconsider </b><font color="Maroon">n</font> =  <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">j</font> as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/><a NAME="E4:59_1_2"/>
<font color="Maroon">n</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="binop_2.html#K7">-</a> 0
 <b>by </b><i/>;<br/><a NAME="E5:59_1_2"/><b>then </b>
<font color="Maroon">n</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T39">NAT_1:39</a></i>;<br/><a NAME="E6:59_1_2"/><b>then </b>
( <font color="Maroon">n</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 or <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> 1 )
 <b>by </b><i><a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><a NAME="E7:59_1_2"/><b>then </b>
(  <a href="binop_2.html#K7">-</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a>  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">j</font></span>)</span> or  <a href="binop_2.html#K7">-</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> )
 <b>by </b><i><a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/><b>hence </b><a NAME="E8:59_1_2"/>
( <font color="Maroon">j</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 or <font color="Maroon">j</font> <a href="hidden.html#R1">=</a>  <a href="binop_2.html#K7">-</a> 1 or <font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;</a>  <a href="binop_2.html#K7">-</a> 1 )
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

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