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<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font> be   <a href="supinf_1.html#NM3" title="SUPINF_1:NM.3">R_eal</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span></span><br/>



<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:44_1"/>
( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">x</font> or <font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1_1"><b>suppose </b></a><a NAME="E1:44_1_1"/>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span></span><br/><div class="add"><a NAME="E2:44_1_1"/><b>then </b>
( <font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <b>by </b><i><a class="ref" href="extreal1.html#T22" title="EXTREAL1:th.22">EXTREAL1:22</a>, <a class="ref" href="extreal1.html#D3" title="EXTREAL1:def.3">EXTREAL1:def 3</a></i>;<br/><a NAME="E3:44_1_1"/><b>then </b>
( <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <b>by </b><i><a class="ref" href="extreal1.html#T22" title="EXTREAL1:th.22">EXTREAL1:22</a>, <a class="ref" href="extreal1.html#D3" title="EXTREAL1:def.3">EXTREAL1:def 3</a></i>;<br/><b>hence </b><a NAME="E4:44_1_1"/>
<span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1_2"><b>suppose </b></a><a NAME="E1:44_1_2"/><i><font color="Green" title="E27">A1</font></i>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span></span><br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="44_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_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="E1:44_1_2_1_1"/>
( <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">y</font> or <font color="Maroon" title="c2">y</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:44_1_2_1_1_1"/>
<font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span></span><br/><div class="add"><a NAME="E2:44_1_2_1_1_1"/><b>then </b>
( <font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <b>by </b><i><a class="ref" href="extreal1.html#T22" title="EXTREAL1:th.22">EXTREAL1:22</a>, <a class="ref" href="extreal1.html#D3" title="EXTREAL1:def.3">EXTREAL1:def 3</a></i>;<br/><a NAME="E3:44_1_2_1_1_1"/><b>then </b>
( <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <b>by </b><i><a class="ref" href="extreal1.html#T22" title="EXTREAL1:th.22">EXTREAL1:22</a>, <a class="ref" href="extreal1.html#D3" title="EXTREAL1:def.3">EXTREAL1:def 3</a></i>;<br/><b>hence </b><a NAME="E4:44_1_2_1_1_1"/>
<span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:44_1_2_1_1_2"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span></span><br/><div class="add"><a NAME="E2:44_1_2_1_1_2"/><b>then </b>
(  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font> &amp; <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font> &amp; <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">y</font> )
 <b>by </b><i><a class="txt" href="extreal2.html#E1:44_1_2"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="extreal1.html#T20" title="EXTREAL1:th.20">EXTREAL1:20</a>, <a class="ref" href="extreal1.html#D3" title="EXTREAL1:def.3">EXTREAL1:def 3</a></i>;<br/><b>hence </b><a NAME="E3:44_1_2_1_1_2"/>
<span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span>
 <b>by </b><i><a class="ref" href="extreal1.html#D3" title="EXTREAL1:def.3">EXTREAL1:def 3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1_2_1_1_3"><b>suppose </b></a><a NAME="E1:44_1_2_1_1_3"/><i><font color="Green" title="E28">A2</font></i>: 
<font color="Maroon" title="c2">y</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span></span><br/><div class="add"><a NAME="E2:44_1_2_1_1_3"/><b>then </b>
( <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font> &amp; <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <font color="Maroon" title="c2">y</font> )
 <b>by </b><i><a class="txt" href="extreal2.html#E1:44_1_2"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="extreal1.html#D3" title="EXTREAL1:def.3">EXTREAL1:def 3</a></i>;<br/><a NAME="E3:44_1_2_1_1_3"/><b>then </b><i><font color="Green" title="E29">A3</font></i>: 
<span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font></span>)</span>
 <b>by </b><i><a class="ref" href="extreal1.html#T26" title="EXTREAL1:th.26">EXTREAL1:26</a></i>;<br/><a NAME="E4:44_1_2_1_1_3"/>
<font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="extreal2.html#E1:44_1_2"><i><font color="Green" title="E27">A1</font></i></a>, <a class="txt" href="extreal2.html#E1:44_1_2_1_1_3"><i><font color="Green" title="E28">A2</font></i></a>, <a class="ref" href="extreal1.html#T21" title="EXTREAL1:th.21">EXTREAL1:21</a></i>;<br/><b>hence </b><a NAME="E5:44_1_2_1_1_3"/>
<span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span>
 <b>by </b><i><a class="txt" href="extreal2.html#E3:44_1_2_1_1_3"><i><font color="Green" title="E29">A3</font></i></a>, <a class="ref" href="extreal1.html#D3" title="EXTREAL1:def.3">EXTREAL1:def 3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:44_1_2"/>
<span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1_3"><b>suppose </b></a><a NAME="E1:44_1_3"/><i><font color="Green" title="E27">A4</font></i>: 
<font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span></span><br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="44_1_3_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_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="E1:44_1_3_1_1"/>
( <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">y</font> or <font color="Maroon" title="c2">y</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1_3_1_1_1"><b>suppose </b></a><a NAME="E1:44_1_3_1_1_1"/>
<font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span></span><br/><div class="add"><a NAME="E2:44_1_3_1_1_1"/><b>then </b>
( <font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <b>by </b><i><a class="ref" href="extreal1.html#T22" title="EXTREAL1:th.22">EXTREAL1:22</a>, <a class="ref" href="extreal1.html#D3" title="EXTREAL1:def.3">EXTREAL1:def 3</a></i>;<br/><a NAME="E3:44_1_3_1_1_1"/><b>then </b>
( <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <b>by </b><i><a class="ref" href="extreal1.html#T22" title="EXTREAL1:th.22">EXTREAL1:22</a>, <a class="ref" href="extreal1.html#D3" title="EXTREAL1:def.3">EXTREAL1:def 3</a></i>;<br/><b>hence </b><a NAME="E4:44_1_3_1_1_1"/>
<span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1_3_1_1_2"><b>suppose </b></a><a NAME="E1:44_1_3_1_1_2"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span></span><br/><div class="add"><a NAME="E2:44_1_3_1_1_2"/><b>then </b>
( not  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font> &amp; <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">y</font> )
 <b>by </b><i><a class="txt" href="extreal2.html#E1:44_1_3"><i><font color="Green" title="E27">A4</font></i></a>, <a class="ref" href="extreal1.html#T21" title="EXTREAL1:th.21">EXTREAL1:21</a>, <a class="ref" href="extreal1.html#D3" title="EXTREAL1:def.3">EXTREAL1:def 3</a></i>;<br/><a NAME="E3:44_1_3_1_1_2"/><b>then </b>
( <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font></span>)</span> &amp; <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font> )
 <b>by </b><i><a class="txt" href="extreal2.html#E1:44_1_3"><i><font color="Green" title="E27">A4</font></i></a>, <a class="ref" href="extreal1.html#D3" title="EXTREAL1:def.3">EXTREAL1:def 3</a></i>;<br/><b>hence </b><a NAME="E4:44_1_3_1_1_2"/>
<span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span>
 <b>by </b><i><a class="ref" href="extreal1.html#T26" title="EXTREAL1:th.26">EXTREAL1:26</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1_3_1_1_3"><b>suppose </b></a><a NAME="E1:44_1_3_1_1_3"/>
<font color="Maroon" title="c2">y</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span></span><br/><div class="add"><a NAME="E2:44_1_3_1_1_3"/><b>then </b><i><font color="Green" title="E28">A5</font></i>: 
(  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font> &amp; <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <font color="Maroon" title="c2">y</font> )
 <b>by </b><i><a class="txt" href="extreal2.html#E1:44_1_3"><i><font color="Green" title="E27">A4</font></i></a>, <a class="ref" href="extreal1.html#T20" title="EXTREAL1:th.20">EXTREAL1:20</a>, <a class="ref" href="extreal1.html#D3" title="EXTREAL1:def.3">EXTREAL1:def 3</a></i>;<br/><a NAME="E3:44_1_3_1_1_3"/><b>then </b>
( <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font> &amp; <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <font color="Maroon" title="c2">y</font></span>)</span> )
 <b>by </b><i><a class="txt" href="extreal2.html#E1:44_1_3"><i><font color="Green" title="E27">A4</font></i></a>, <a class="ref" href="extreal1.html#D3" title="EXTREAL1:def.3">EXTREAL1:def 3</a></i>;<br/><b>then </b><span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> = 
 <a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <span class="p2">(<span class="default"><a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="extreal1.html#T26" title="EXTREAL1:th.26">EXTREAL1:26</a></i>
<br/>.= 
 <a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="extreal1.html#T26" title="EXTREAL1:th.26">EXTREAL1:26</a></i>
;<br/><b>hence </b><a NAME="E5:44_1_3_1_1_3"/>
<span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span>
 <b>by </b><i><a class="txt" href="extreal2.html#E2:44_1_3_1_1_3"><i><font color="Green" title="E28">A5</font></i></a>, <a class="ref" href="extreal1.html#D3" title="EXTREAL1:def.3">EXTREAL1:def 3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:44_1_3"/>
<span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c2">y</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div>

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