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<span class="kw">let </span><font color="Maroon" title="c1">y</font>, <font color="Maroon" title="c2">x</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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xxreal_0.html#K1" title="XXREAL_0:func.1">+infty</a>  &amp; <font color="Maroon" title="c1">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xxreal_0.html#K2" title="XXREAL_0:func.2">-infty</a>  &amp; <font color="Maroon" title="c1">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="xxreal_3.html#K6" title="XXREAL_3:func.6">/</a> <font color="Maroon" title="c1">y</font></span>)</span> <a href="xxreal_3.html#K4" title="XXREAL_3:func.4">*</a> <font color="Maroon" title="c1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:10"/><span class="lab"><font color="Green" title="E9">A1</font></span>: 
( <font color="Maroon" title="c1">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xxreal_0.html#K1" title="XXREAL_0:func.1">+infty</a>  &amp; <font color="Maroon" title="c1">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xxreal_0.html#K2" title="XXREAL_0:func.2">-infty</a>  )
 <span class="kw">and </span><br/><a NAME="E2:10"/><span class="lab"><font color="Green" title="E10">A2</font></span>: 
<font color="Maroon" title="c1">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="xxreal_3.html#K6" title="XXREAL_3:func.6">/</a> <font color="Maroon" title="c1">y</font></span>)</span> <a href="xxreal_3.html#K4" title="XXREAL_3:func.4">*</a> <font color="Maroon" title="c1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font></span><br/>

<span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="xxreal_3.html#K6" title="XXREAL_3:func.6">/</a> <font color="Maroon" title="c1">y</font></span>)</span> <a href="xxreal_3.html#K4" title="XXREAL_3:func.4">*</a> <font color="Maroon" title="c1">y</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="xxreal_3.html#K4" title="XXREAL_3:func.4">*</a> <span class="p2">(<span class="default">1 <a href="xxreal_3.html#K6" title="XXREAL_3:func.6">/</a> <font color="Maroon" title="c1">y</font></span>)</span></span>)</span> <a href="xxreal_3.html#K4" title="XXREAL_3:func.4">*</a> <font color="Maroon" title="c1">y</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_3.html#T81" title="XXREAL_3:th.81">XXREAL_3:81</a></span>
<br/>.= 
<font color="Maroon" title="c2">x</font> <a href="xxreal_3.html#K4" title="XXREAL_3:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xxreal_3.html#K6" title="XXREAL_3:func.6">/</a> <font color="Maroon" title="c1">y</font></span>)</span> <a href="xxreal_3.html#K4" title="XXREAL_3:func.4">*</a> <font color="Maroon" title="c1">y</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_3.html#T66" title="XXREAL_3:th.66">XXREAL_3:66</a></span>
<br/>.= 
<font color="Maroon" title="c2">x</font> <a href="xxreal_3.html#K4" title="XXREAL_3:func.4">*</a> 1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="ref" href="xxreal_3.html#T87" title="XXREAL_3:th.87">XXREAL_3:87</a></span>
<br/>.= 
<font color="Maroon" title="c2">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_3.html#T81" title="XXREAL_3:th.81">XXREAL_3:81</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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