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<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">z</font> be   <a href="supinf_1.html#NM3" title="SUPINF_1:NM.3">R_eal</a>;<br/>

<b>assume </b><a NAME="E1:18"/><i><font color="Green" title="E13">A1</font></i>: 
(  <a href="supinf_2.html#K1" title="SUPINF_2:func.1">0.</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">x</font> &amp; <font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">z</font> )
 ;<br/>

<a NAME="E2:18"/><b>then </b><i><font color="Green" title="E14">A2</font></i>: 
<font color="Maroon" title="c1">x</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>
 
<b>by </b><i><a class="ref" href="measure6.html#T15" target="_self" title="MEASURE6:th.15">Th15</a></i>;<br/>
<a NAME="E3:18"/>
 <a href="supinf_2.html#K1" title="SUPINF_2:func.1">0.</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">z</font> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c1">x</font>
 
<b>by </b><i><a class="txt" href="measure6.html#E1:18"><i><font color="Green" title="E13">A1</font></i></a>, <a class="ref" href="measure6.html#T19" target="_self" title="MEASURE6:th.19">Th19</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c3">y</font> being   <a href="supinf_1.html#NM3" title="SUPINF_1:NM.3">R_eal</a><b> such that </b><br/><a NAME="E5:18"/><i><font color="Green" title="E15">A3</font></i>: 
(  <a href="supinf_2.html#K1" title="SUPINF_2:func.1">0.</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c3">y</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">z</font> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c1">x</font> )
 <b>by </b><i><a class="ref" href="measure6.html#T23" target="_self" title="MEASURE6:th.23">Th23</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c3">y</font>
;<br/>

<a NAME="E6:18"/><i><font color="Green" title="E16">A4</font></i>: 
<font color="Maroon" title="c1">x</font> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <font color="Maroon" title="c3">y</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">x</font> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c1">x</font></span>)</span>
 
<b>by </b><i><a class="txt" href="measure6.html#E2:18"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="measure6.html#E5:18"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="measure6.html#T11" target="_self" title="MEASURE6:th.11">Th11</a></i>;<br/>
<a NAME="E7:18"/><i><font color="Green" title="E17">A5</font></i>: 
<font color="Maroon" title="c1">x</font> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">z</font>
 
<b>by </b><i><a class="txt" href="measure6.html#E2:18"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="measure6.html#T8" target="_self" title="MEASURE6:th.8">Th8</a></i>;<br/>
<a NAME="E8:18"/><i><font color="Green" title="E18">A6</font></i>: 
<font color="Maroon" title="c1">x</font> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">z</font>
 
<b>by </b><i><a class="txt" href="measure6.html#E2:18"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="measure6.html#E5:18"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="measure6.html#T8" target="_self" title="MEASURE6:th.8">Th8</a></i>;<br/>
<a NAME="E9:18"/>
<font color="Maroon" title="c3">y</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>
 
<b>by </b><i><a class="txt" href="measure6.html#E5:18"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="measure6.html#T15" target="_self" title="MEASURE6:th.15">Th15</a></i>;<br/>
<b>hence </b><a NAME="E10:18"/>
(  <a href="supinf_2.html#K1" title="SUPINF_2:func.1">0.</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c1">x</font> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <font color="Maroon" title="c3">y</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">z</font> &amp; <font color="Maroon" title="c3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="supinf_1.html#K3" title="SUPINF_1:func.3">REAL</a>  )
 <b>by </b><i><a class="txt" href="measure6.html#E5:18"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="measure6.html#E6:18"><i><font color="Green" title="E16">A4</font></i></a>, <a class="txt" href="measure6.html#E7:18"><i><font color="Green" title="E17">A5</font></i></a>, <a class="txt" href="measure6.html#E8:18"><i><font color="Green" title="E18">A6</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/>


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