<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">B</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c1">n</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c3">t</font>, <font color="Maroon" title="c4">s</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>







<b>assume </b><a NAME="E1:90"/><i><font color="Green" title="E39">A1</font></i>: 
( <font color="Maroon" title="c2">B</font> is <a href="jordan1.html#V1" title="JORDAN1:attr.1">convex</a> &amp; 0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c3">t</font> &amp; 0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c4">s</font> )
 ;<br/>

<a NAME="E2:90"/><b>then </b><i><font color="Green" title="E40">A2</font></i>: 
0 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T10" title="XREAL_1:th.10">XREAL_1:10</a></i>;<br/>
<a NAME="E3:90"/><b>then </b><i><font color="Green" title="E41">A3</font></i>: 
0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span>
 
<b>by </b><i><a class="ref" href="real_2.html#T127" title="REAL_2:th.127">REAL_2:127</a>, <a class="txt" href="mathmorp.html#E1:90"><i><font color="Green" title="E39">A1</font></i></a></i>;<br/>
<a NAME="E4:90"/>
<font color="Maroon" title="c4">s</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T31" title="XREAL_1:th.31">XREAL_1:31</a>, <a class="txt" href="mathmorp.html#E1:90"><i><font color="Green" title="E39">A1</font></i></a></i>;<br/>
<a NAME="E5:90"/><b>then </b>
<font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span>
 
<b>by </b><i><a class="ref" href="real_1.html#T73" title="REAL_1:th.73">REAL_1:73</a>, <a class="txt" href="mathmorp.html#E1:90"><i><font color="Green" title="E39">A1</font></i></a></i>;<br/>
<a NAME="E6:90"/><b>then </b><i><font color="Green" title="E42">A4</font></i>: 
<font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> 1
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T60" title="XCMPLX_1:th.60">XCMPLX_1:60</a>, <a class="txt" href="mathmorp.html#E2:90"><i><font color="Green" title="E40">A2</font></i></a></i>;<br/>
<b>thus </b><a NAME="E7:90"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="mathmorp.html#K7" title="MATHMORP:func.7">(.)</a> <font color="Maroon" title="c2">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="mathmorp.html#K7" title="MATHMORP:func.7">(.)</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="mathmorp.html#K4" title="MATHMORP:func.4">(+)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">t</font> <a href="mathmorp.html#K7" title="MATHMORP:func.7">(.)</a> <font color="Maroon" title="c2">B</font></span>)</span>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="90_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:90_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="mathmorp.html#K7" title="MATHMORP:func.7">(.)</a> <font color="Maroon" title="c2">B</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c6">b</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c1">n</font></span>)</span><b> such that </b><br/><a NAME="E3:90_1"/><i><font color="Green" title="E43">A5</font></i>: 
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c6">b</font> &amp; <font color="Maroon" title="c6">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B</font> )
 ;<br/>
<a NAME="E4:90_1"/><i><font color="Green" title="E44">A6</font></i>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c6">b</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">t</font> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c6">b</font></span>)</span>
 
<b>by </b><i><a class="ref" href="euclid.html#T37" title="EUCLID:th.37">EUCLID:37</a>, <a class="txt" href="mathmorp.html#E3:90_1"><i><font color="Green" title="E43">A5</font></i></a></i>;<br/>
<a NAME="E5:90_1"/><i><font color="Green" title="E45">A7</font></i>: 
<font color="Maroon" title="c4">s</font> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c6">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">s</font> <a href="mathmorp.html#K7" title="MATHMORP:func.7">(.)</a> <font color="Maroon" title="c2">B</font>
 
<b>by </b><i><a class="txt" href="mathmorp.html#E3:90_1"><i><font color="Green" title="E43">A5</font></i></a></i>;<br/>
<a NAME="E6:90_1"/>
<font color="Maroon" title="c3">t</font> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c6">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">t</font> <a href="mathmorp.html#K7" title="MATHMORP:func.7">(.)</a> <font color="Maroon" title="c2">B</font>
 
<b>by </b><i><a class="txt" href="mathmorp.html#E3:90_1"><i><font color="Green" title="E43">A5</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:90_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="mathmorp.html#K7" title="MATHMORP:func.7">(.)</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="mathmorp.html#K4" title="MATHMORP:func.4">(+)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">t</font> <a href="mathmorp.html#K7" title="MATHMORP:func.7">(.)</a> <font color="Maroon" title="c2">B</font></span>)</span>
 <b>by </b><i><a class="txt" href="mathmorp.html#E4:90_1"><i><font color="Green" title="E44">A6</font></i></a>, <a class="txt" href="mathmorp.html#E5:90_1"><i><font color="Green" title="E45">A7</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E8:90"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="mathmorp.html#K7" title="MATHMORP:func.7">(.)</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="mathmorp.html#K4" title="MATHMORP:func.4">(+)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">t</font> <a href="mathmorp.html#K7" title="MATHMORP:func.7">(.)</a> <font color="Maroon" title="c2">B</font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c6">s1</font>, <font color="Maroon" title="c7">s2</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c1">n</font></span>)</span><b> such that </b><br/><a NAME="E10:90"/><i><font color="Green" title="E43">A8</font></i>: 
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s1</font> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <font color="Maroon" title="c7">s2</font> &amp; <font color="Maroon" title="c6">s1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">s</font> <a href="mathmorp.html#K7" title="MATHMORP:func.7">(.)</a> <font color="Maroon" title="c2">B</font> &amp; <font color="Maroon" title="c7">s2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">t</font> <a href="mathmorp.html#K7" title="MATHMORP:func.7">(.)</a> <font color="Maroon" title="c2">B</font> )
 ;<br/>
<b>consider </b><font color="Maroon" title="c8">b1</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c1">n</font></span>)</span><b> such that </b><br/><a NAME="E12:90"/><i><font color="Green" title="E44">A9</font></i>: 
( <font color="Maroon" title="c6">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c8">b1</font> &amp; <font color="Maroon" title="c8">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B</font> )
 <b>by </b><i><a class="txt" href="mathmorp.html#E10:90"><i><font color="Green" title="E43">A8</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c9">b2</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c1">n</font></span>)</span><b> such that </b><br/><a NAME="E14:90"/><i><font color="Green" title="E45">A10</font></i>: 
( <font color="Maroon" title="c7">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">t</font> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c9">b2</font> &amp; <font color="Maroon" title="c9">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B</font> )
 <b>by </b><i><a class="txt" href="mathmorp.html#E10:90"><i><font color="Green" title="E43">A8</font></i></a></i>;<br/>
<a NAME="E15:90"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c8">b1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c9">b2</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B</font>
 
<b>by </b><i><a class="txt" href="mathmorp.html#E1:90"><i><font color="Green" title="E39">A1</font></i></a>, <a class="txt" href="mathmorp.html#E3:90"><i><font color="Green" title="E41">A3</font></i></a>, <a class="txt" href="mathmorp.html#E6:90"><i><font color="Green" title="E42">A4</font></i></a>, <a class="txt" href="mathmorp.html#E12:90"><i><font color="Green" title="E44">A9</font></i></a>, <a class="txt" href="mathmorp.html#E14:90"><i><font color="Green" title="E45">A10</font></i></a>, <a class="ref" href="mathmorp.html#D11" target="_self" title="MATHMORP:def.11">Def11</a></i>;<br/>
<a NAME="E16:90"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c8">b1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c9">b2</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Olive" title="b1">zz</font></span>)</span> where <font color="Olive" title="b1">zz</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c1">n</font></span>)</span> : <font color="Olive" title="b1">zz</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B</font> </span>}</span> 
 
;<br/>
<a NAME="E17:90"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c8">b1</font></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c9">b2</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="mathmorp.html#K7" title="MATHMORP:func.7">(.)</a> <font color="Maroon" title="c2">B</font>
 
<b>by </b><i><a class="ref" href="euclid.html#T36" title="EUCLID:th.36">EUCLID:36</a></i>;<br/>
<a NAME="E18:90"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c8">b1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c9">b2</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="mathmorp.html#K7" title="MATHMORP:func.7">(.)</a> <font color="Maroon" title="c2">B</font>
 
<b>by </b><i><a class="ref" href="euclid.html#T34" title="EUCLID:th.34">EUCLID:34</a></i>;<br/>
<a NAME="E19:90"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c8">b1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c9">b2</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="mathmorp.html#K7" title="MATHMORP:func.7">(.)</a> <font color="Maroon" title="c2">B</font>
 
<b>by </b><i><a class="ref" href="euclid.html#T34" title="EUCLID:th.34">EUCLID:34</a></i>;<br/>
<a NAME="E20:90"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c8">b1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c9">b2</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="mathmorp.html#K7" title="MATHMORP:func.7">(.)</a> <font color="Maroon" title="c2">B</font>
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T88" title="XCMPLX_1:th.88">XCMPLX_1:88</a>, <a class="txt" href="mathmorp.html#E2:90"><i><font color="Green" title="E40">A2</font></i></a></i>;<br/>
<a NAME="E21:90"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c8">b1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c9">b2</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="mathmorp.html#K7" title="MATHMORP:func.7">(.)</a> <font color="Maroon" title="c2">B</font>
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T60" title="XCMPLX_1:th.60">XCMPLX_1:60</a>, <a class="txt" href="mathmorp.html#E2:90"><i><font color="Green" title="E40">A2</font></i></a></i>;<br/>
<a NAME="E22:90"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c8">b1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c9">b2</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="mathmorp.html#K7" title="MATHMORP:func.7">(.)</a> <font color="Maroon" title="c2">B</font>
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T121" title="XCMPLX_1:th.121">XCMPLX_1:121</a></i>;<br/>
<b>hence </b><a NAME="E23:90"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="mathmorp.html#K7" title="MATHMORP:func.7">(.)</a> <font color="Maroon" title="c2">B</font>
 <b>by </b><i><a class="txt" href="mathmorp.html#E10:90"><i><font color="Green" title="E43">A8</font></i></a>, <a class="txt" href="mathmorp.html#E12:90"><i><font color="Green" title="E44">A9</font></i></a>, <a class="txt" href="mathmorp.html#E14:90"><i><font color="Green" title="E45">A10</font></i></a>, <a class="ref" href="xcmplx_1.html#T88" title="XCMPLX_1:th.88">XCMPLX_1:88</a>, <a class="txt" href="mathmorp.html#E2:90"><i><font color="Green" title="E40">A2</font></i></a></i>;<br/>


</div>
