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<div class="add">

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

<b>assume </b><a NAME="E1:24"/><i><font color="Green" title="E17">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>
 ;<br/>

<a NAME="E2:24"/>
for <font color="Olive" title="b1">y</font> being <a href="xxreal_0.html#V1" title="XXREAL_0:attr.1">ext-real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   st <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="measure6.html#K2" title="MEASURE6:func.2">Seg</a> <font color="Maroon" title="c1">x</font> holds <br/><font color="Olive" title="b1">y</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">y</font> be  <a href="xxreal_0.html#V1" title="XXREAL_0:attr.1">ext-real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>

<b>assume </b><a NAME="E1:24_1"/><i><font color="Green" title="E18">A2</font></i>: 
<font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="measure6.html#K2" title="MEASURE6:func.2">Seg</a> <font color="Maroon" title="c1">x</font>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c3">y</font> = <font color="Maroon" title="c2">y</font> as   <a href="supinf_1.html#NM3" title="SUPINF_1:NM.3">R_eal</a> <b>by </b><i><a class="ref" href="xxreal_0.html#D1" title="XXREAL_0:def.1">XXREAL_0:def 1</a></i>;<br/>
<a NAME="E3:24_1"/>
(  <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="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="c1">x</font> )
 
<b>by </b><i><a class="txt" href="measure6.html#E1:24"><i><font color="Green" title="E17">A1</font></i></a>, <a class="ref" href="measure6.html#D2" target="_self" title="MEASURE6:def.2">Def2</a>, <a class="txt" href="measure6.html#E1:24_1"><i><font color="Green" title="E18">A2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:24_1"/>
<font color="Maroon" title="c2">y</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">x</font>
 <b>by </b><i><a class="ref" href="measure6.html#T22" target="_self" title="MEASURE6:th.22">Th22</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:24"/><b>then </b>
<font color="Maroon" title="c1">x</font> is    <a href="supinf_1.html#M1" title="SUPINF_1:mode.1">majorant</a> of  <a href="measure6.html#K2" title="MEASURE6:func.2">Seg</a> <font color="Maroon" title="c1">x</font>
 
<b>by </b><i><a class="ref" href="supinf_1.html#D9" title="SUPINF_1:def.9">SUPINF_1:def 9</a></i>;<br/>
<b>hence </b><a NAME="E4:24"/>
 <a href="measure6.html#K3" title="MEASURE6:func.3">len</a> <font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">x</font>
 <b>by </b><i><a class="ref" href="supinf_1.html#D16" title="SUPINF_1:def.16">SUPINF_1:def 16</a></i>;<br/>


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