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<b>let </b><font color="Maroon">x</font> be   <a href="supinf_1.html#NM3">R_eal</a>;<br/>

<a NAME="E1:3"/><i><font color="Green">E18</font></i>: 
 <a href="measure6.html#K1">R_EAL</a> 1 <a href="hidden.html#R1">=</a>  <a href="mesfunc1.html#K10">1.</a> 
 
<b>by </b><i><a class="ref" href="measure6.html#D1">MEASURE6:def 1</a>, <a class="ref" href="mesfunc1.html#D8">MESFUNC1:def 8</a></i>;<br/>
<a NAME="E2:3"/><i><font color="Green">E19</font></i>: 
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="mesfunc1.html#K10">1.</a> 
 
<b>by </b><i><a class="ref" href="mesfunc1.html#D8">MESFUNC1:def 8</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:3_1"/>
( <font color="Maroon">x</font> is   <a href="real_1.html#NM1">Real</a> or <font color="Maroon">x</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>  )
 </span><b>by </b><i><a class="ref" href="extreal1.html#T1">EXTREAL1:1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_1_1"><b>suppose </b></a><a NAME="E1:3_1_1"/>
<font color="Maroon">x</font> is   <a href="real_1.html#NM1">Real</a>
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">a</font> = <font color="Maroon">x</font> as   <a href="real_1.html#NM1">Real</a> ;<br/><a NAME="E3:3_1_1"/>
<a href="mesfunc1.html#K10">1.</a>  <a href="extreal1.html#K2">*</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 1 <a href="real_1.html#K4">*</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="extreal1.html#T13">EXTREAL1:13</a>, <a class="ref" href="mesfunc1.html#D8">MESFUNC1:def 8</a></i>;<br/><b>hence </b><a NAME="E4:3_1_1"/>
( <a href="mesfunc1.html#K10">1.</a>  <a href="extreal1.html#K2">*</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <span class="p1">(<span class="default"><a href="measure6.html#K1">R_EAL</a> 1</span>)</span> <a href="extreal1.html#K2">*</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> )
 <b>by </b><i><a class="ref" href="measure6.html#D1">MEASURE6:def 1</a>, <a class="ref" href="mesfunc1.html#D8">MESFUNC1:def 8</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_1_2"><b>suppose </b></a><a NAME="E1:3_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="supinf_1.html#K1">+infty</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:3_1_2"/>
( <a href="mesfunc1.html#K10">1.</a>  <a href="extreal1.html#K2">*</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <span class="p1">(<span class="default"><a href="measure6.html#K1">R_EAL</a> 1</span>)</span> <a href="extreal1.html#K2">*</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> )
 <b>by </b><i>, , <a class="ref" href="extreal1.html#D1">EXTREAL1:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_1_3"><b>suppose </b></a><a NAME="E1:3_1_3"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="supinf_1.html#K2">-infty</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:3_1_3"/>
( <a href="mesfunc1.html#K10">1.</a>  <a href="extreal1.html#K2">*</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <span class="p1">(<span class="default"><a href="measure6.html#K1">R_EAL</a> 1</span>)</span> <a href="extreal1.html#K2">*</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> )
 <b>by </b><i>, , <a class="ref" href="extreal1.html#D1">EXTREAL1:def 1</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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