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<b>let </b><font color="Maroon">x</font> be   <a href="supinf_1.html#NM3">R_eal</a>, <font color="Maroon">y</font> be   <a href="supinf_1.html#NM3">R_eal</a>;<br/><b>let </b><font color="Maroon">e</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>



<b>assume </b><a NAME="E1:3"/><i><font color="Green">E35</font></i>: 
<span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="supinf_2.html#K4">-</a> <font color="Maroon">y</font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">e</font>
 ;<br/>

<a NAME="E2:3"/>
( <font color="Maroon">x</font> <a href="supinf_2.html#K4">-</a> <font color="Maroon">y</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="supinf_2.html#K4">-</a> <font color="Maroon">y</font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> &amp; <font color="Maroon">y</font> <a href="supinf_2.html#K4">-</a> <font color="Maroon">x</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="supinf_2.html#K4">-</a> <font color="Maroon">y</font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> )
 
<b>by </b><i>, <a class="ref" href="extreal2.html#T57">EXTREAL2:57</a></i>;<br/>
<a NAME="E3:3"/><b>then </b>
( <font color="Maroon">x</font> <a href="supinf_2.html#K4">-</a> <font color="Maroon">y</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="measure6.html#K1">R_EAL</a> <font color="Maroon">e</font> &amp; <font color="Maroon">y</font> <a href="supinf_2.html#K4">-</a> <font color="Maroon">x</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">e</font> )
 
<b>by </b><i>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<b>hence </b><a NAME="E4:3"/>
( ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="supinf_1.html#K1">+infty</a>  &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="supinf_1.html#K1">+infty</a>  ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="supinf_1.html#K2">-infty</a>  &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="supinf_1.html#K2">-infty</a>  ) or ( <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="supinf_1.html#K1">+infty</a>  &amp; <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="supinf_1.html#K2">-infty</a>  &amp; <font color="Maroon">y</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="supinf_1.html#K1">+infty</a>  &amp; <font color="Maroon">y</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="supinf_1.html#K2">-infty</a>  ) )
 <b>by </b><i><a class="ref" href="extreal2.html#T29">EXTREAL2:29</a></i>;<br/>


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