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<a NAME="E1:44_1_1"/>
( ( <font color="Maroon" title="c1">i</font> <a href="xreal_0.html#K1" title="XREAL_0:func.1">-'</a> <font color="Maroon" title="c2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c2">j</font> &amp;  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">i</font> <a href="xreal_0.html#K1" title="XREAL_0:func.1">-'</a> <font color="Maroon" title="c2">j</font> ) or <font color="Maroon" title="c1">i</font> <a href="xreal_0.html#K1" title="XREAL_0:func.1">-'</a> <font color="Maroon" title="c2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<b>by </b><i><a class="ref" href="xreal_0.html#D2" title="XREAL_0:def.2">XREAL_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E2:44_1_1"/>
<font color="Maroon" title="c1">i</font> <a href="xreal_0.html#K1" title="XREAL_0:func.1">-'</a> <font color="Maroon" title="c2">j</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">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" title="INT_1:th.16">INT_1:16</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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