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<b>let </b><font color="Maroon">f</font> be   <a href="struct_0.html#NM6">Function</a> of <a href="topmetr.html#K5">I[01]</a> ,<span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>, <font color="Maroon">g</font> be   <a href="struct_0.html#NM6">Function</a> of <a href="topmetr.html#K5">I[01]</a> ,<span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon">a</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> , <font color="Maroon">b</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> , <font color="Maroon">c</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> , <font color="Maroon">d</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">O</font> be   <a href="pre_topc.html#NM2">Point</a> of <a href="topmetr.html#K5">I[01]</a> , <font color="Maroon">I</font> be   <a href="pre_topc.html#NM2">Point</a> of <a href="topmetr.html#K5">I[01]</a> ;<br/>





<b>assume </b><a NAME="E1:65"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">O</font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">f</font> is <a href="pre_topc.html#V5">continuous</a> &amp; <font color="Maroon">f</font> is <a href="funct_1.html#V2">one-to-one</a> &amp; <font color="Maroon">g</font> is <a href="pre_topc.html#V5">continuous</a> &amp; <font color="Maroon">g</font> is <a href="funct_1.html#V2">one-to-one</a> &amp; <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">I</font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">c</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> <a href="euclid.html#K22">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">c</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">I</font></span>)</span> <a href="euclid.html#K22">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">I</font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">d</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">I</font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">a</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">a</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">I</font></span>)</span> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">I</font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">b</font> &amp; <font color="Maroon">c</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">d</font> &amp; ( for <font color="Olive">r</font> being  <a href="pre_topc.html#NM2">Point</a> of <a href="topmetr.html#K5">I[01]</a>   holds <br/>(  not <font color="Maroon">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">r</font></span>)</span> <a href="euclid.html#K21">`1</a>  or  not <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">r</font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">b</font> or  not <font color="Maroon">c</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">r</font></span>)</span> <a href="euclid.html#K22">`2</a>  or  not <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">r</font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">d</font> ) ) &amp; ( for <font color="Olive">r</font> being  <a href="pre_topc.html#NM2">Point</a> of <a href="topmetr.html#K5">I[01]</a>   holds <br/>(  not <font color="Maroon">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Olive">r</font></span>)</span> <a href="euclid.html#K21">`1</a>  or  not <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Olive">r</font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">b</font> or  not <font color="Maroon">c</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Olive">r</font></span>)</span> <a href="euclid.html#K22">`2</a>  or  not <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Olive">r</font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">d</font> ) ) )
 ;<br/>

<a NAME="E2:65"/><b>then </b><i><font color="Green">E28</font></i>: 
<font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="xreal_1.html#T52">XREAL_1:52</a></i>;<br/>
<a NAME="E3:65"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T52">XREAL_1:52</a></i>;<br/>
<b>set </b><font color="Maroon">A</font> = 2 <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">B</font> = 1 <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">C</font> = 2 <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">D</font> = 1 <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span>;<br/>
<a NAME="E4:65"/><i><font color="Green">E43</font></i>: 
2 <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="jgraph_2.html#T10" target="_self">Th10</a>, <a class="ref" href="real_2.html#T127">REAL_2:127</a></i>;<br/>
<a NAME="E5:65"/><i><font color="Green">E44</font></i>: 
2 <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i>, <a class="ref" href="real_2.html#T127">REAL_2:127</a></i>;<br/>
<b>set </b><font color="Maroon">ff</font> =  <a href="jgraph_2.html#K2" target="_self">AffineMap</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span>,<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span>,<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span>;<br/>
<a NAME="E6:65"/><i><font color="Green">E45</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="jgraph_2.html#K2" target="_self">AffineMap</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p4">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E7:65"/><i><font color="Green">E46</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="topmetr.html#K5">I[01]</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E8:65"/><i><font color="Green">E47</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="topmetr.html#K5">I[01]</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E9:65"/><i><font color="Green">E48</font></i>: 
 <a href="jgraph_2.html#K2" target="_self">AffineMap</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span>,<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span>,<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i>, , </i>;<br/>
<b>reconsider </b><font color="Maroon">f2</font> = <span class="p1">(<span class="default"><a href="jgraph_2.html#K2" target="_self">AffineMap</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p4">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font>, <font color="Maroon">g2</font> = <span class="p1">(<span class="default"><a href="jgraph_2.html#K2" target="_self">AffineMap</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p4">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">g</font> as   <a href="struct_0.html#NM6">Function</a> of <a href="topmetr.html#K5">I[01]</a> ,<span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> ;<br/>
<a NAME="E11:65"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">f2</font> is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i>, <a class="ref" href="tops_2.html#T58">TOPS_2:58</a></i>;<br/>
<a NAME="E12:65"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">g2</font> is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i>, <a class="ref" href="tops_2.html#T58">TOPS_2:58</a></i>;<br/>
<a NAME="E13:65"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">f2</font> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i>, , <a class="ref" href="funct_1.html#T46">FUNCT_1:46</a></i>;<br/>
<a NAME="E14:65"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">g2</font> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i>, , <a class="ref" href="funct_1.html#T46">FUNCT_1:46</a></i>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>] <b>means </b>(  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">a<sub>1</sub></font> <a href="euclid.html#K21">`1</a>  &amp; <font color="Maroon">a<sub>1</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">a<sub>1</sub></font> <a href="euclid.html#K22">`2</a>  &amp; <font color="Maroon">a<sub>1</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 );<br/>
<b>reconsider </b><font color="Maroon">K0</font> = <span class="p1">{<span class="default"> <font color="Olive">p</font> where <font color="Olive">p</font> is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">p</font>] </span>}</span>  as   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <b>from </b><i><a class="ref" href="jgraph_2.html#S1" target="_self">JGRAPH_2:sch 1</a>();<br/></i>
<i><font color="Green">E54</font></i>: <font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font> = 
<span class="p1">(<span class="default"><a href="jgraph_2.html#K2" target="_self">AffineMap</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p4">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span>
<b>by </b><i>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p5">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p5">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p5">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p5">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
<b>by </b><i>, <a class="txt" href="jgraph_2.html#E24:65"><i><font color="Green">E68</font></i></a></i>
;<br/>
<i><font color="Green">E55</font></i>: <font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">I</font> = 
<span class="p1">(<span class="default"><a href="jgraph_2.html#K2" target="_self">AffineMap</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p4">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">I</font></span>)</span>
<b>by </b><i>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p5">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p5">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p5">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">I</font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p5">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
<b>by </b><i>, <a class="txt" href="jgraph_2.html#E24:65"><i><font color="Green">E68</font></i></a></i>
;<br/>
<i><font color="Green">E57</font></i>: <font color="Maroon">g2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font> = 
<span class="p1">(<span class="default"><a href="jgraph_2.html#K2" target="_self">AffineMap</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p4">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span>
<b>by </b><i>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p5">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p5">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p5">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p5">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
<b>by </b><i>, <a class="txt" href="jgraph_2.html#E24:65"><i><font color="Green">E68</font></i></a></i>
;<br/>
<i><font color="Green">E58</font></i>: <font color="Maroon">g2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">I</font> = 
<span class="p1">(<span class="default"><a href="jgraph_2.html#K2" target="_self">AffineMap</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p4">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">I</font></span>)</span>
<b>by </b><i>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p5">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">I</font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p5">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p5">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p5">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
<b>by </b><i>, <a class="txt" href="jgraph_2.html#E24:65"><i><font color="Green">E68</font></i></a></i>
;<br/>
<a NAME="E20:65"/><i><font color="Green">E59</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_5"><b>proof </b></a><div class="add">

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> <a href="euclid.html#K21">`1</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="jgraph_2.html#T14" target="_self">Th14</a>, <a class="ref" href="euclid.html#T56">EUCLID:56</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T75">XCMPLX_1:75</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="jgraph_2.html#T10" target="_self">Th10</a>, <a class="ref" href="xcmplx_1.html#T60">XCMPLX_1:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T121">XCMPLX_1:121</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T63">XCMPLX_1:63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span>

<br/>.= 
 <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T188">XCMPLX_1:188</a></i>
<br/>.= 
 <a href="real_1.html#K1">-</a> 1
<b>by </b><i><a class="ref" href="jgraph_2.html#T10" target="_self">Th10</a>, <a class="ref" href="xcmplx_1.html#T60">XCMPLX_1:60</a></i>
;<br/>


</div><b>end;</b></div>
<i><font color="Green">E60</font></i>: <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">I</font></span>)</span> <a href="euclid.html#K21">`1</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="jgraph_2.html#T15" target="_self">Th15</a>, <a class="ref" href="euclid.html#T56">EUCLID:56</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K3">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T75">XCMPLX_1:75</a></i>
<br/>.= 
1

;<br/>
<i><font color="Green">E65</font></i>: <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> <a href="euclid.html#K22">`2</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="jgraph_2.html#T18" target="_self">Th18</a>, <a class="ref" href="euclid.html#T56">EUCLID:56</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K3">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T75">XCMPLX_1:75</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K3">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="xcmplx_1.html#T60">XCMPLX_1:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K3">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T121">XCMPLX_1:121</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K3">*</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T63">XCMPLX_1:63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span>

<br/>.= 
 <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T188">XCMPLX_1:188</a></i>
<br/>.= 
 <a href="real_1.html#K1">-</a> 1
<b>by </b><i>, <a class="ref" href="xcmplx_1.html#T60">XCMPLX_1:60</a></i>
;<br/>
<i><font color="Green">E67</font></i>: <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">I</font></span>)</span> <a href="euclid.html#K22">`2</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="jgraph_2.html#T19" target="_self">Th19</a>, <a class="ref" href="euclid.html#T56">EUCLID:56</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K3">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T75">XCMPLX_1:75</a></i>
<br/>.= 
1

;<br/>
<a NAME="E24:65"/><i><font color="Green">E68</font></i>: 
(  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> <a href="euclid.html#K22">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">I</font></span>)</span> <a href="euclid.html#K22">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">I</font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_9"><b>proof </b></a><div class="add">

<b>reconsider </b><font color="Maroon">s0</font> = <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> <a href="euclid.html#K22">`2</a>  as   <a href="real_1.html#NM1">Real</a> ;<br/>
<a NAME="E2:65_9"/><i><font color="Green">E70</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s0</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">s0</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_9_1"><b>proof </b></a><div class="add">

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> <a href="euclid.html#K22">`2</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">s0</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="jgraph_2.html#T14" target="_self">Th14</a>, <a class="ref" href="euclid.html#T56">EUCLID:56</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s0</font> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T75">XCMPLX_1:75</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s0</font> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="xcmplx_1.html#T60">XCMPLX_1:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s0</font> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T121">XCMPLX_1:121</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s0</font> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T63">XCMPLX_1:63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s0</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">s0</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span>

;<br/>


</div><b>end;</b></div>
<a NAME="E3:65_9"/>
<font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">s0</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font>
 
<b>by </b><i><a class="txt" href="jgraph_2.html#E2:65_9"><i><font color="Green">E70</font></i></a>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<a NAME="E4:65_9"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">s0</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">s0</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E5:65_9"/><b>then </b><i><font color="Green">E143</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s0</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">s0</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<i><font color="Green">E148</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span>

<br/>.= 
 <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T188">XCMPLX_1:188</a></i>
<br/>.= 
 <a href="real_1.html#K1">-</a> 1
<b>by </b><i>, <a class="ref" href="xcmplx_1.html#T60">XCMPLX_1:60</a></i>
;<br/>
<a NAME="E7:65_9"/>
<font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">s0</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font>
 
<b>by </b><i><a class="txt" href="jgraph_2.html#E2:65_9"><i><font color="Green">E70</font></i></a>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<a NAME="E8:65_9"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">s0</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">s0</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E9:65_9"/><b>then </b>
<span class="p1">(<span class="default">0 <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s0</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">s0</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<a NAME="E10:65_9"/><b>then </b><i><font color="Green">E149</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s0</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">s0</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="real_1.html#T73">REAL_1:73</a></i>;<br/>
<b>reconsider </b><font color="Maroon">s1</font> = <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">I</font></span>)</span> <a href="euclid.html#K22">`2</a>  as   <a href="real_1.html#NM1">Real</a> ;<br/>
<a NAME="E12:65_9"/><i><font color="Green">E150</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">I</font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_9_3"><b>proof </b></a><div class="add">

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">I</font></span>)</span> <a href="euclid.html#K22">`2</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">s1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="jgraph_2.html#T15" target="_self">Th15</a>, <a class="ref" href="euclid.html#T56">EUCLID:56</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s1</font> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T75">XCMPLX_1:75</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s1</font> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="xcmplx_1.html#T60">XCMPLX_1:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s1</font> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T121">XCMPLX_1:121</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s1</font> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T63">XCMPLX_1:63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span>

;<br/>


</div><b>end;</b></div>
<a NAME="E13:65_9"/>
<font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">s1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font>
 
<b>by </b><i><a class="txt" href="jgraph_2.html#E2:65_9"><i><font color="Green">E70</font></i></a>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<a NAME="E14:65_9"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E15:65_9"/><b>then </b><i><font color="Green">E151</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">s1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<a NAME="E16:65_9"/>
<font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">s1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font>
 
<b>by </b><i><a class="txt" href="jgraph_2.html#E2:65_9"><i><font color="Green">E70</font></i></a>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<a NAME="E17:65_9"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E18:65_9"/><b>then </b>
<span class="p1">(<span class="default">0 <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">s1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<a NAME="E19:65_9"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="real_1.html#T73">REAL_1:73</a></i>;<br/>
<b>hence </b><a NAME="E20:65_9"/>
(  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> <a href="euclid.html#K22">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">I</font></span>)</span> <a href="euclid.html#K22">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">I</font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 )
 <b>by </b><i>, , , , , <a class="ref" href="jgraph_2.html#T21" target="_self">Th21</a>, , <a class="ref" href="real_1.html#T73">REAL_1:73</a>, <a class="ref" href="xcmplx_1.html#T60">XCMPLX_1:60</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E25:65"/><i><font color="Green">E152</font></i>: 
(  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">I</font></span>)</span> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">I</font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_10"><b>proof </b></a><div class="add">

<b>reconsider </b><font color="Maroon">s0</font> = <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> <a href="euclid.html#K21">`1</a>  as   <a href="real_1.html#NM1">Real</a> ;<br/>
<a NAME="E2:65_10"/><i><font color="Green">E153</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s0</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">s0</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_10_1"><b>proof </b></a><div class="add">

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> <a href="euclid.html#K21">`1</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">s0</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="jgraph_2.html#T18" target="_self">Th18</a>, <a class="ref" href="euclid.html#T56">EUCLID:56</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s0</font> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T75">XCMPLX_1:75</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s0</font> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="jgraph_2.html#T10" target="_self">Th10</a>, <a class="ref" href="xcmplx_1.html#T60">XCMPLX_1:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s0</font> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T121">XCMPLX_1:121</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s0</font> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T63">XCMPLX_1:63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s0</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">s0</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span>

;<br/>


</div><b>end;</b></div>
<a NAME="E3:65_10"/>
<font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">s0</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font>
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<a NAME="E4:65_10"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">s0</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">s0</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E5:65_10"/><b>then </b><i><font color="Green">E154</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s0</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">s0</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<i><font color="Green">E155</font></i>: <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span>

<br/>.= 
 <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T188">XCMPLX_1:188</a></i>
<br/>.= 
 <a href="real_1.html#K1">-</a> 1
<b>by </b><i><a class="ref" href="jgraph_2.html#T10" target="_self">Th10</a>, <a class="ref" href="xcmplx_1.html#T60">XCMPLX_1:60</a></i>
;<br/>
<a NAME="E7:65_10"/>
<font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">s0</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font>
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<a NAME="E8:65_10"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">s0</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">s0</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E9:65_10"/><b>then </b>
<span class="p1">(<span class="default">0 <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s0</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">s0</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<a NAME="E10:65_10"/><b>then </b><i><font color="Green">E156</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s0</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">s0</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span>
 
<b>by </b><i><a class="ref" href="jgraph_2.html#T10" target="_self">Th10</a>, <a class="ref" href="real_1.html#T73">REAL_1:73</a></i>;<br/>
<b>reconsider </b><font color="Maroon">s1</font> = <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">I</font></span>)</span> <a href="euclid.html#K21">`1</a>  as   <a href="real_1.html#NM1">Real</a> ;<br/>
<a NAME="E12:65_10"/><i><font color="Green">E157</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">I</font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_10_3"><b>proof </b></a><div class="add">

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">I</font></span>)</span> <a href="euclid.html#K21">`1</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">s1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="jgraph_2.html#T19" target="_self">Th19</a>, <a class="ref" href="euclid.html#T56">EUCLID:56</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s1</font> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T75">XCMPLX_1:75</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s1</font> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="jgraph_2.html#T10" target="_self">Th10</a>, <a class="ref" href="xcmplx_1.html#T60">XCMPLX_1:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s1</font> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T121">XCMPLX_1:121</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s1</font> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T63">XCMPLX_1:63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span>

;<br/>


</div><b>end;</b></div>
<a NAME="E13:65_10"/>
<font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">s1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font>
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<a NAME="E14:65_10"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E15:65_10"/><b>then </b><i><font color="Green">E158</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">s1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<a NAME="E16:65_10"/>
<font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">s1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font>
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<a NAME="E17:65_10"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E18:65_10"/><b>then </b>
<span class="p1">(<span class="default">0 <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">s1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<a NAME="E19:65_10"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span>
 
<b>by </b><i><a class="ref" href="jgraph_2.html#T10" target="_self">Th10</a>, <a class="ref" href="real_1.html#T73">REAL_1:73</a></i>;<br/>
<b>hence </b><a NAME="E20:65_10"/>
(  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">I</font></span>)</span> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">I</font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 )
 <b>by </b><i><a class="ref" href="jgraph_2.html#T10" target="_self">Th10</a>, , , , <a class="ref" href="jgraph_2.html#T21" target="_self">Th21</a>, , <a class="ref" href="jgraph_2.html#T22" target="_self">Th22</a>, <a class="ref" href="real_1.html#T73">REAL_1:73</a>, <a class="ref" href="xcmplx_1.html#T60">XCMPLX_1:60</a></i>;<br/>


</div><b>end;</b></div>
<div><i><font color="Green">E159</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="65_11"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:65_11"/>
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">f2</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">K0</font>
 ;<br/><b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:65_11"/><i><font color="Green">E160</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">f2</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K0</font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/><b>reconsider </b><font color="Maroon">q</font> = <font color="Maroon">x</font> as   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">p</font> being   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span><b> such that </b><br/><a NAME="E6:65_11"/><i><font color="Green">E161</font></i>: 
( <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">p</font> <a href="euclid.html#K21">`1</a>  &amp; <font color="Maroon">p</font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">p</font> <a href="euclid.html#K22">`2</a>  &amp; <font color="Maroon">p</font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 )
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">z</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E8:65_11"/><i><font color="Green">E162</font></i>: 
( <font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f2</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> )
 <b>by </b><i>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/><b>reconsider </b><font color="Maroon">u</font> = <font color="Maroon">z</font> as   <a href="pre_topc.html#NM2">Point</a> of <a href="topmetr.html#K5">I[01]</a>  <b>by </b><i><a class="ref" href="jgraph_2.html#T21" target="_self">Th21</a></i>;<br/><b>reconsider </b><font color="Maroon">t</font> = <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">u</font> as   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> ;<br/><a NAME="E11:65_11"/><i><font color="Green">E163</font></i>: 
<span class="p1">(<span class="default"><a href="jgraph_2.html#K2" target="_self">AffineMap</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p4">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p5">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p5">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p5">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p5">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
 <b>by </b><i><a class="txt" href="jgraph_2.html#E24:65"><i><font color="Green">E68</font></i></a></i>;<br/><a NAME="E12:65_11"/>
<span class="p1">(<span class="default"><a href="jgraph_2.html#K2" target="_self">AffineMap</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p4">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font>
 <b>by </b><i>, <a class="ref" href="jgraph_2.html#T21" target="_self">Th21</a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>;<br/><a NAME="E13:65_11"/><b>then </b><i><font color="Green">E164</font></i>: 
(  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 )
 <b>by </b><i>, , <a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/><a NAME="E14:65_11"/><i><font color="Green">E165</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_11_1"><b>proof </b></a><div class="add">

<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T75">XCMPLX_1:75</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="jgraph_2.html#T10" target="_self">Th10</a>, <a class="ref" href="xcmplx_1.html#T60">XCMPLX_1:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T121">XCMPLX_1:121</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T63">XCMPLX_1:63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span>

;<br/>


</div><b>end;</b></div><a NAME="E15:65_11"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span>
 <b>by </b><i><a class="ref" href="jgraph_2.html#T10" target="_self">Th10</a>, <a class="ref" href="jgraph_2.html#T22" target="_self">Th22</a>, <a class="ref" href="xreal_1.html#T70">XREAL_1:70</a></i>;<br/><a NAME="E16:65_11"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span>
 <b>by </b><i><a class="ref" href="jgraph_2.html#T10" target="_self">Th10</a>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/><a NAME="E17:65_11"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/><a NAME="E18:65_11"/><b>then </b>
<span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2
 <b>by </b><i><a class="ref" href="real_1.html#T73">REAL_1:73</a></i>;<br/><a NAME="E19:65_11"/><b>then </b><i><font color="Green">E166</font></i>: 
<font color="Maroon">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> 
 <b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E20:65_11"/>
1 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span>
 <b>by </b><i><a class="ref" href="jgraph_2.html#T10" target="_self">Th10</a>, <a class="ref" href="jgraph_2.html#T22" target="_self">Th22</a>, , <a class="ref" href="xreal_1.html#T70">XREAL_1:70</a></i>;<br/><a NAME="E21:65_11"/><b>then </b>
1 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span>
 <b>by </b><i><a class="ref" href="jgraph_2.html#T10" target="_self">Th10</a>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/><a NAME="E22:65_11"/><b>then </b>
<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/><a NAME="E23:65_11"/><b>then </b>
0 <a href="real_1.html#K6">/</a> 2 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> 2
 <b>by </b><i><a class="ref" href="real_1.html#T73">REAL_1:73</a></i>;<br/><a NAME="E24:65_11"/><b>then </b><i><font color="Green">E167</font></i>: 
0 <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> 
 <b>by </b><i><a class="ref" href="xreal_1.html#T21">XREAL_1:21</a></i>;<br/><i><font color="Green">E168</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T75">XCMPLX_1:75</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="xcmplx_1.html#T60">XCMPLX_1:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T121">XCMPLX_1:121</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T63">XCMPLX_1:63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span>

;<br/><a NAME="E26:65_11"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="jgraph_2.html#T22" target="_self">Th22</a>, <a class="ref" href="xreal_1.html#T70">XREAL_1:70</a></i>;<br/><a NAME="E27:65_11"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/><a NAME="E28:65_11"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/><a NAME="E29:65_11"/><b>then </b>
<span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2
 <b>by </b><i><a class="ref" href="real_1.html#T73">REAL_1:73</a></i>;<br/><a NAME="E30:65_11"/><b>then </b><i><font color="Green">E169</font></i>: 
<font color="Maroon">c</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> 
 <b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E31:65_11"/>
1 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="jgraph_2.html#T22" target="_self">Th22</a>, , <a class="ref" href="xreal_1.html#T70">XREAL_1:70</a></i>;<br/><a NAME="E32:65_11"/><b>then </b>
1 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/><a NAME="E33:65_11"/><b>then </b>
<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/><a NAME="E34:65_11"/><b>then </b>
0 <a href="real_1.html#K6">/</a> 2 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> 2
 <b>by </b><i><a class="ref" href="real_1.html#T73">REAL_1:73</a></i>;<br/><a NAME="E35:65_11"/><b>then </b>
0 <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">d</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> 
 <b>by </b><i><a class="ref" href="xreal_1.html#T21">XREAL_1:21</a></i>;<br/><b>hence </b><a NAME="E36:65_11"/>
contradiction
 <b>by </b><i>, , , </i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_12"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:65_12"/>
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">g2</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">K0</font>
 ;<br/><b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:65_12"/><i><font color="Green">E170</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">g2</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K0</font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/><b>reconsider </b><font color="Maroon">q</font> = <font color="Maroon">x</font> as   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">p</font> being   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span><b> such that </b><br/><a NAME="E6:65_12"/><i><font color="Green">E171</font></i>: 
( <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">p</font> <a href="euclid.html#K21">`1</a>  &amp; <font color="Maroon">p</font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">p</font> <a href="euclid.html#K22">`2</a>  &amp; <font color="Maroon">p</font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 )
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">z</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E8:65_12"/><i><font color="Green">E172</font></i>: 
( <font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">g2</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> )
 <b>by </b><i>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/><b>reconsider </b><font color="Maroon">u</font> = <font color="Maroon">z</font> as   <a href="pre_topc.html#NM2">Point</a> of <a href="topmetr.html#K5">I[01]</a>  <b>by </b><i><a class="ref" href="jgraph_2.html#T21" target="_self">Th21</a></i>;<br/><b>reconsider </b><font color="Maroon">t</font> = <font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">u</font> as   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> ;<br/><a NAME="E11:65_12"/><i><font color="Green">E173</font></i>: 
<span class="p1">(<span class="default"><a href="jgraph_2.html#K2" target="_self">AffineMap</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p4">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p5">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p5">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p5">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p5">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
 <b>by </b><i><a class="txt" href="jgraph_2.html#E24:65"><i><font color="Green">E68</font></i></a></i>;<br/><a NAME="E12:65_12"/>
<span class="p1">(<span class="default"><a href="jgraph_2.html#K2" target="_self">AffineMap</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p4">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font>
 <b>by </b><i>, <a class="ref" href="jgraph_2.html#T21" target="_self">Th21</a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>;<br/><a NAME="E13:65_12"/><b>then </b><i><font color="Green">E183</font></i>: 
(  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 )
 <b>by </b><i>, , <a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/><i><font color="Green">E184</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T75">XCMPLX_1:75</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="jgraph_2.html#T10" target="_self">Th10</a>, <a class="ref" href="xcmplx_1.html#T60">XCMPLX_1:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T121">XCMPLX_1:121</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T63">XCMPLX_1:63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span>

;<br/><a NAME="E15:65_12"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span>
 <b>by </b><i><a class="ref" href="jgraph_2.html#T10" target="_self">Th10</a>, <a class="ref" href="jgraph_2.html#T22" target="_self">Th22</a>, <a class="ref" href="xreal_1.html#T70">XREAL_1:70</a></i>;<br/><a NAME="E16:65_12"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span>
 <b>by </b><i><a class="ref" href="jgraph_2.html#T10" target="_self">Th10</a>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/><a NAME="E17:65_12"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/><a NAME="E18:65_12"/><b>then </b>
<span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2
 <b>by </b><i><a class="ref" href="real_1.html#T73">REAL_1:73</a></i>;<br/><a NAME="E19:65_12"/><b>then </b><i><font color="Green">E185</font></i>: 
<font color="Maroon">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> 
 <b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E20:65_12"/>
1 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span>
 <b>by </b><i><a class="ref" href="jgraph_2.html#T10" target="_self">Th10</a>, <a class="ref" href="jgraph_2.html#T22" target="_self">Th22</a>, , <a class="ref" href="xreal_1.html#T70">XREAL_1:70</a></i>;<br/><a NAME="E21:65_12"/><b>then </b>
1 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span>
 <b>by </b><i><a class="ref" href="jgraph_2.html#T10" target="_self">Th10</a>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/><a NAME="E22:65_12"/><b>then </b>
<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/><a NAME="E23:65_12"/><b>then </b>
0 <a href="real_1.html#K6">/</a> 2 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> 2
 <b>by </b><i><a class="ref" href="real_1.html#T73">REAL_1:73</a></i>;<br/><a NAME="E24:65_12"/><b>then </b><i><font color="Green">E186</font></i>: 
0 <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">t</font> <a href="euclid.html#K21">`1</a> 
 <b>by </b><i><a class="ref" href="xreal_1.html#T21">XREAL_1:21</a></i>;<br/><i><font color="Green">E187</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T75">XCMPLX_1:75</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="xcmplx_1.html#T60">XCMPLX_1:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T121">XCMPLX_1:121</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T63">XCMPLX_1:63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span>

;<br/><a NAME="E26:65_12"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="jgraph_2.html#T22" target="_self">Th22</a>, <a class="ref" href="xreal_1.html#T70">XREAL_1:70</a></i>;<br/><a NAME="E27:65_12"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/><a NAME="E28:65_12"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/><a NAME="E29:65_12"/><b>then </b>
<span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2
 <b>by </b><i><a class="ref" href="real_1.html#T73">REAL_1:73</a></i>;<br/><a NAME="E30:65_12"/><b>then </b><i><font color="Green">E188</font></i>: 
<font color="Maroon">c</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> 
 <b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E31:65_12"/>
1 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="jgraph_2.html#T22" target="_self">Th22</a>, , <a class="ref" href="xreal_1.html#T70">XREAL_1:70</a></i>;<br/><a NAME="E32:65_12"/><b>then </b>
1 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/><a NAME="E33:65_12"/><b>then </b>
<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/><a NAME="E34:65_12"/><b>then </b>
0 <a href="real_1.html#K6">/</a> 2 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> 2
 <b>by </b><i><a class="ref" href="real_1.html#T73">REAL_1:73</a></i>;<br/><a NAME="E35:65_12"/><b>then </b>
0 <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">d</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">t</font> <a href="euclid.html#K22">`2</a> 
 <b>by </b><i><a class="ref" href="xreal_1.html#T21">XREAL_1:21</a></i>;<br/><b>hence </b><a NAME="E36:65_12"/>
contradiction
 <b>by </b><i>, , , </i>;<br/></div><b>end;</b></div>
<a NAME="E28:65"/><b>then </b>
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">f2</font> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">g2</font>
 
<b>by </b><i>, , <a class="ref" href="jgraph_2.html#T11" target="_self">Th11</a>, <a class="ref" href="jgraph_2.html#T12" target="_self">Th12</a>, <a class="ref" href="jgraph_2.html#T13" target="_self">Th13</a>, , <a class="ref" href="jgraph_2.html#T20" target="_self">Th20</a>, , , , , , </i>;<br/>
<a NAME="E29:65"/><b>then </b><i><font color="Green">E189</font></i>: 
<span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">f2</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">g2</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<b>consider </b><font color="Maroon">y</font> being    <a href="subset_1.html#M1">Element</a> of <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">f2</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">g2</font></span>)</span>;<br/>
<a NAME="E31:65"/><i><font color="Green">E190</font></i>: 
( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">f2</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">g2</font> )
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E33:65"/><i><font color="Green">E191</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f2</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E34:65"/><i><font color="Green">E255</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="jgraph_2.html#K2" target="_self">AffineMap</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p4">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font></span>)</span>
 
<b>by </b><i><a class="ref" href="jgraph_2.html#T21" target="_self">Th21</a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>;<br/>
<b>consider </b><font color="Maroon">x2</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E36:65"/><i><font color="Green">E256</font></i>: 
( <font color="Maroon">x2</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">g2</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x2</font> )
 <b>by </b><i>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E37:65"/><i><font color="Green">E257</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="jgraph_2.html#K2" target="_self">AffineMap</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p4">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="jgraph_2.html#T22" target="_self">Th22</a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>;<br/>
<a NAME="E38:65"/>
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">f2</font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T44">RELAT_1:44</a></i>;<br/>
<a NAME="E39:65"/><b>then </b><i><font color="Green">E258</font></i>: 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="ref" href="jgraph_2.html#T21" target="_self">Th21</a>, <a class="ref" href="funct_1.html#T12">FUNCT_1:12</a></i>;<br/>
<a NAME="E40:65"/>
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">g2</font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">g</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T44">RELAT_1:44</a></i>;<br/>
<a NAME="E41:65"/><b>then </b><i><font color="Green">E259</font></i>: 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x2</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">g</font>
 
<b>by </b><i><a class="ref" href="jgraph_2.html#T22" target="_self">Th22</a>, <a class="ref" href="funct_1.html#T12">FUNCT_1:12</a></i>;<br/>
<a NAME="E42:65"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x2</font>
 
<b>by </b><i>, , , , , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/>
<a NAME="E43:65"/><b>then </b>
<span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">g</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i>, , <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>hence </b><a NAME="E44:65"/>
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">g</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>


</div>
