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<div class="add">

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



<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:45_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 0 or 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">x</font> or <font color="Maroon">x</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1"><b>suppose </b></a><a NAME="E1:45_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:45_1_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="extreal1.html#K2">*</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">x</font></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a> 0 )
 <b>by </b><i><a class="ref" href="extreal1.html#T22">EXTREAL1:22</a>, <a class="ref" href="extreal1.html#D3">EXTREAL1:def 3</a></i>;<br/><a NAME="E3:45_1_1"/><b>then </b>
( <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="extreal1.html#K2">*</a> <font color="Maroon">y</font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">x</font></span><a href="extreal1.html#K4">.|</a></span> <a href="extreal1.html#K2">*</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">y</font></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a> 0 )
 <b>by </b><i><a class="ref" href="extreal1.html#T22">EXTREAL1:22</a>, <a class="ref" href="extreal1.html#D3">EXTREAL1:def 3</a></i>;<br/><b>hence </b><a NAME="E4:45_1_1"/>
<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="extreal1.html#K2">*</a> <font color="Maroon">y</font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">x</font></span><a href="extreal1.html#K4">.|</a></span> <a href="extreal1.html#K2">*</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">y</font></span><a href="extreal1.html#K4">.|</a></span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_2"><b>suppose </b></a><a NAME="E1:45_1_2"/><i><font color="Green">E18</font></i>: 
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">x</font>
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="45_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:45_1_2_1_1"/>
( <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> 0 or 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">y</font> or <font color="Maroon">y</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:45_1_2_1_1_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:45_1_2_1_1_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="extreal1.html#K2">*</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">y</font></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a> 0 )
 <b>by </b><i><a class="ref" href="extreal1.html#T22">EXTREAL1:22</a>, <a class="ref" href="extreal1.html#D3">EXTREAL1:def 3</a></i>;<br/><a NAME="E3:45_1_2_1_1_1"/><b>then </b>
( <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="extreal1.html#K2">*</a> <font color="Maroon">y</font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">x</font></span><a href="extreal1.html#K4">.|</a></span> <a href="extreal1.html#K2">*</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">y</font></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a> 0 )
 <b>by </b><i><a class="ref" href="extreal1.html#T22">EXTREAL1:22</a>, <a class="ref" href="extreal1.html#D3">EXTREAL1:def 3</a></i>;<br/><b>hence </b><a NAME="E4:45_1_2_1_1_1"/>
<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="extreal1.html#K2">*</a> <font color="Maroon">y</font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">x</font></span><a href="extreal1.html#K4">.|</a></span> <a href="extreal1.html#K2">*</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">y</font></span><a href="extreal1.html#K4">.|</a></span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:45_1_2_1_1_2"/>
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">y</font>
 ;<br/><div class="add"><a NAME="E2:45_1_2_1_1_2"/><b>then </b>
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">x</font> <a href="extreal1.html#K2">*</a> <font color="Maroon">y</font> &amp; <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">x</font></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">y</font></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 <b>by </b><i><a class="txt" href="extreal2.html#E17"><i><font color="Green">Lemma29</font></i></a>, <a class="ref" href="extreal1.html#T20">EXTREAL1:20</a>, <a class="ref" href="extreal1.html#D3">EXTREAL1:def 3</a></i>;<br/><b>hence </b><a NAME="E3:45_1_2_1_1_2"/>
<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="extreal1.html#K2">*</a> <font color="Maroon">y</font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">x</font></span><a href="extreal1.html#K4">.|</a></span> <a href="extreal1.html#K2">*</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">y</font></span><a href="extreal1.html#K4">.|</a></span>
 <b>by </b><i><a class="ref" href="extreal1.html#D3">EXTREAL1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_2_1_1_3"><b>suppose </b></a><a NAME="E1:45_1_2_1_1_3"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">y</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0
 ;<br/><div class="add"><a NAME="E2:45_1_2_1_1_3"/><b>then </b>
( <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">x</font></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">y</font></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a>  <a href="supinf_2.html#K3">-</a> <font color="Maroon">y</font> )
 <b>by </b><i><a class="txt" href="extreal2.html#E17"><i><font color="Green">Lemma29</font></i></a>, <a class="ref" href="extreal1.html#D3">EXTREAL1:def 3</a></i>;<br/><a NAME="E3:45_1_2_1_1_3"/><b>then </b><i><font color="Green">E20</font></i>: 
<span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">x</font></span><a href="extreal1.html#K4">.|</a></span> <a href="extreal1.html#K2">*</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">y</font></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a>  <a href="supinf_2.html#K3">-</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="extreal1.html#K2">*</a> <font color="Maroon">y</font></span>)</span>
 <b>by </b><i><a class="ref" href="extreal1.html#T26">EXTREAL1:26</a></i>;<br/><a NAME="E4:45_1_2_1_1_3"/>
<font color="Maroon">x</font> <a href="extreal1.html#K2">*</a> <font color="Maroon">y</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0
 <b>by </b><i><a class="txt" href="extreal2.html#E17"><i><font color="Green">Lemma29</font></i></a>, <a class="txt" href="extreal2.html#E19"><i><font color="Green">Lemma30</font></i></a>, <a class="ref" href="extreal1.html#T21">EXTREAL1:21</a></i>;<br/><b>hence </b><a NAME="E5:45_1_2_1_1_3"/>
<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="extreal1.html#K2">*</a> <font color="Maroon">y</font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">x</font></span><a href="extreal1.html#K4">.|</a></span> <a href="extreal1.html#K2">*</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">y</font></span><a href="extreal1.html#K4">.|</a></span>
 <b>by </b><i><a class="txt" href="extreal2.html#E20"><i><font color="Green">Lemma31</font></i></a>, <a class="ref" href="extreal1.html#D3">EXTREAL1:def 3</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:45_1_2"/>
<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="extreal1.html#K2">*</a> <font color="Maroon">y</font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">x</font></span><a href="extreal1.html#K4">.|</a></span> <a href="extreal1.html#K2">*</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">y</font></span><a href="extreal1.html#K4">.|</a></span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_3"><b>suppose </b></a><a NAME="E1:45_1_3"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">x</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="45_1_3_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_3_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:45_1_3_1_1"/>
( <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> 0 or 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">y</font> or <font color="Maroon">y</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_3_1_1_1"><b>suppose </b></a><a NAME="E1:45_1_3_1_1_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:45_1_3_1_1_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="extreal1.html#K2">*</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">y</font></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a> 0 )
 <b>by </b><i><a class="ref" href="extreal1.html#T22">EXTREAL1:22</a>, <a class="ref" href="extreal1.html#D3">EXTREAL1:def 3</a></i>;<br/><a NAME="E3:45_1_3_1_1_1"/><b>then </b>
( <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="extreal1.html#K2">*</a> <font color="Maroon">y</font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">x</font></span><a href="extreal1.html#K4">.|</a></span> <a href="extreal1.html#K2">*</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">y</font></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a> 0 )
 <b>by </b><i><a class="ref" href="extreal1.html#T22">EXTREAL1:22</a>, <a class="ref" href="extreal1.html#D3">EXTREAL1:def 3</a></i>;<br/><b>hence </b><a NAME="E4:45_1_3_1_1_1"/>
<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="extreal1.html#K2">*</a> <font color="Maroon">y</font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">x</font></span><a href="extreal1.html#K4">.|</a></span> <a href="extreal1.html#K2">*</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">y</font></span><a href="extreal1.html#K4">.|</a></span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_3_1_1_2"><b>suppose </b></a><a NAME="E1:45_1_3_1_1_2"/>
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">y</font>
 ;<br/><div class="add"><a NAME="E2:45_1_3_1_1_2"/><b>then </b>
( not 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">x</font> <a href="extreal1.html#K2">*</a> <font color="Maroon">y</font> &amp; <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">y</font></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 <b>by </b><i><a class="txt" href="extreal2.html#E17"><i><font color="Green">Lemma29</font></i></a>, <a class="ref" href="extreal1.html#T21">EXTREAL1:21</a>, <a class="ref" href="extreal1.html#D3">EXTREAL1:def 3</a></i>;<br/><a NAME="E3:45_1_3_1_1_2"/><b>then </b>
( <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="extreal1.html#K2">*</a> <font color="Maroon">y</font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a>  <a href="supinf_2.html#K3">-</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="extreal1.html#K2">*</a> <font color="Maroon">y</font></span>)</span> &amp; <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">x</font></span><a href="extreal1.html#K4">.|</a></span> <a href="extreal1.html#K2">*</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">y</font></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K3">-</a> <font color="Maroon">x</font></span>)</span> <a href="extreal1.html#K2">*</a> <font color="Maroon">y</font> )
 <b>by </b><i><a class="txt" href="extreal2.html#E17"><i><font color="Green">Lemma29</font></i></a>, <a class="ref" href="extreal1.html#D3">EXTREAL1:def 3</a></i>;<br/><b>hence </b><a NAME="E4:45_1_3_1_1_2"/>
<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="extreal1.html#K2">*</a> <font color="Maroon">y</font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">x</font></span><a href="extreal1.html#K4">.|</a></span> <a href="extreal1.html#K2">*</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">y</font></span><a href="extreal1.html#K4">.|</a></span>
 <b>by </b><i><a class="ref" href="extreal1.html#T26">EXTREAL1:26</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_3_1_1_3"><b>suppose </b></a><a NAME="E1:45_1_3_1_1_3"/>
<font color="Maroon">y</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0
 ;<br/><div class="add"><a NAME="E2:45_1_3_1_1_3"/><b>then </b><i><font color="Green">E25</font></i>: 
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">x</font> <a href="extreal1.html#K2">*</a> <font color="Maroon">y</font> &amp; <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">y</font></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a>  <a href="supinf_2.html#K3">-</a> <font color="Maroon">y</font> )
 <b>by </b><i><a class="txt" href="extreal2.html#E17"><i><font color="Green">Lemma29</font></i></a>, <a class="ref" href="extreal1.html#T20">EXTREAL1:20</a>, <a class="ref" href="extreal1.html#D3">EXTREAL1:def 3</a></i>;<br/><a NAME="E3:45_1_3_1_1_3"/><b>then </b>
( <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="extreal1.html#K2">*</a> <font color="Maroon">y</font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="extreal1.html#K2">*</a> <font color="Maroon">y</font> &amp; <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">x</font></span><a href="extreal1.html#K4">.|</a></span> <a href="extreal1.html#K2">*</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">y</font></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K3">-</a> <font color="Maroon">x</font></span>)</span> <a href="extreal1.html#K2">*</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K3">-</a> <font color="Maroon">y</font></span>)</span> )
 <b>by </b><i><a class="txt" href="extreal2.html#E17"><i><font color="Green">Lemma29</font></i></a>, <a class="ref" href="extreal1.html#D3">EXTREAL1:def 3</a></i>;<br/><b>then </b><span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">x</font></span><a href="extreal1.html#K4">.|</a></span> <a href="extreal1.html#K2">*</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">y</font></span><a href="extreal1.html#K4">.|</a></span> = 
 <a href="supinf_2.html#K3">-</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="extreal1.html#K2">*</a> <span class="p2">(<span class="default"><a href="supinf_2.html#K3">-</a> <font color="Maroon">y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="extreal1.html#T26">EXTREAL1:26</a></i>
<br/>.= 
 <a href="supinf_2.html#K3">-</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K3">-</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="extreal1.html#K2">*</a> <font color="Maroon">y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="extreal1.html#T26">EXTREAL1:26</a></i>
;<br/><b>hence </b><a NAME="E5:45_1_3_1_1_3"/>
<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="extreal1.html#K2">*</a> <font color="Maroon">y</font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">x</font></span><a href="extreal1.html#K4">.|</a></span> <a href="extreal1.html#K2">*</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">y</font></span><a href="extreal1.html#K4">.|</a></span>
 <b>by </b><i><a class="txt" href="extreal2.html#E19"><i><font color="Green">Lemma30</font></i></a>, <a class="ref" href="extreal1.html#D3">EXTREAL1:def 3</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:45_1_3"/>
<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="extreal1.html#K2">*</a> <font color="Maroon">y</font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">x</font></span><a href="extreal1.html#K4">.|</a></span> <a href="extreal1.html#K2">*</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><font color="Maroon">y</font></span><a href="extreal1.html#K4">.|</a></span>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

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