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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>, <font color="Maroon">t</font> be   <a href="supinf_1.html#NM3">R_eal</a>;<br/>

<b>assume </b><a NAME="E1:5"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">t</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="supinf_1.html#K2">-infty</a>  &amp; <font color="Maroon">t</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="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">y</font> )
 ;<br/>

<a NAME="E2:5"/><b>then </b><i><font color="Green">E37</font></i>: 
<font color="Maroon">x</font> <a href="supinf_2.html#K2">+</a> <font color="Maroon">t</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">y</font> <a href="supinf_2.html#K2">+</a> <font color="Maroon">t</font>
 
<b>by </b><i><a class="ref" href="supinf_2.html#T14">SUPINF_2:14</a></i>;<br/>
<a NAME="E3:5"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">t</font> <a href="supinf_2.html#K4">-</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="extreal1.html#T9">EXTREAL1:9</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:5_1"/>
<font color="Maroon">x</font> <a href="supinf_2.html#K2">+</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> <a href="supinf_2.html#K2">+</a> <font color="Maroon">t</font>
 ;<br/><a NAME="E2:5_1"/><b>then </b>
<font color="Maroon">x</font> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="supinf_2.html#K4">-</a> <font color="Maroon">t</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="supinf_2.html#K2">+</a> <font color="Maroon">t</font></span>)</span> <a href="supinf_2.html#K4">-</a> <font color="Maroon">t</font>
 <b>by </b><i>, <a class="ref" href="extreal1.html#T11">EXTREAL1:11</a></i>;<br/><a NAME="E3:5_1"/><b>then </b>
<font color="Maroon">x</font> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><a href="measure6.html#K1">R_EAL</a> 0</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="supinf_2.html#K4">-</a> <font color="Maroon">t</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="extreal1.html#T11">EXTREAL1:11</a></i>;<br/><a NAME="E4:5_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><a href="measure6.html#K1">R_EAL</a> 0</span>)</span>
 <b>by </b><i>, <a class="ref" href="supinf_2.html#T18">SUPINF_2:18</a></i>;<br/><b>hence </b><a NAME="E5:5_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="supinf_2.html#T18">SUPINF_2:18</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:5"/>
<font color="Maroon">x</font> <a href="supinf_2.html#K2">+</a> <font color="Maroon">t</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">y</font> <a href="supinf_2.html#K2">+</a> <font color="Maroon">t</font>
 <b>by </b><i>, <a class="ref" href="supinf_1.html#T22">SUPINF_1:22</a></i>;<br/>


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