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

<b>let </b><font color="Maroon">p1</font> be   <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">p2</font> be   <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">p3</font> be   <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">p4</font> be   <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/><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">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>assume </b><a NAME="E1:104"/><i><font color="Green">E29</font></i>: 
( <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; <font color="Maroon">p1</font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">p2</font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">p3</font> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">p4</font> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">c</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p1</font> <a href="euclid.html#K22">`2</a>  &amp; <font color="Maroon">p1</font> <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> <font color="Maroon">p2</font> <a href="euclid.html#K22">`2</a>  &amp; <font color="Maroon">p2</font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">p4</font> <a href="euclid.html#K21">`1</a>  &amp; <font color="Maroon">p4</font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">p3</font> <a href="euclid.html#K21">`1</a>  &amp; <font color="Maroon">p3</font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> &amp; <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">p3</font> &amp; <font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> &amp; <font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">p4</font> &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;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font> <a href="tarski.html#R1">c=</a>  <a href="jgraph_6.html#K2">closed_inside_of_rectangle</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">g</font> <a href="tarski.html#R1">c=</a>  <a href="jgraph_6.html#K2">closed_inside_of_rectangle</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font> )
 ;<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> =  <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#K2">+</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>;<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> =  <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#K2">+</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>;<br/>
<a NAME="E2:104"/>
<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="jgraph_7.html#T42" target="_self">Th42</a>, <a class="ref" href="xreal_1.html#T52">XREAL_1:52</a></i>;<br/>
<a NAME="E3:104"/><b>then </b><i><font color="Green">E30</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="real_2.html#T127">REAL_2:127</a></i>;<br/>
<a NAME="E4:104"/>
<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="jgraph_7.html#T42" target="_self">Th42</a>, <a class="ref" href="xreal_1.html#T52">XREAL_1:52</a></i>;<br/>
<a NAME="E5:104"/><b>then </b><i><font color="Green">E32</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">h</font> =  <a href="jgraph_2.html#K2">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"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K2">+</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></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"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K2">+</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></span>)</span>;<br/>
<a NAME="E6:104"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">p4</font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="jgraph_7.html#T42" target="_self">Th42</a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E7:104"/><i><font color="Green">E81</font></i>: 
<font color="Maroon">p3</font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="jgraph_7.html#T42" target="_self">Th42</a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E8:104"/><i><font color="Green">E100</font></i>: 
(  <a href="jgraph_2.html#K2">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"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K2">+</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></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"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K2">+</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></span>)</span> <a href="tops_2.html#NR1" target="_self">is_homeomorphism</a>  &amp; ( for <font color="Olive">p11</font>, <font color="Olive">p21</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>  st <font color="Olive">p11</font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">p21</font> <a href="euclid.html#K21">`1</a>  holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jgraph_2.html#K2">AffineMap</a> <span class="p3">(<span class="default">2 <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 class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">a</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 class="p3">(<span class="default">2 <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 class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c</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> <a href="funct_2.html#K3">.</a> <font color="Olive">p11</font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jgraph_2.html#K2">AffineMap</a> <span class="p3">(<span class="default">2 <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 class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">a</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 class="p3">(<span class="default">2 <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 class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c</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> <a href="funct_2.html#K3">.</a> <font color="Olive">p21</font></span>)</span> <a href="euclid.html#K21">`1</a>  ) )
 
<b>by </b><i><a class="ref" href="jgraph_7.html#T8" target="_self">Th8</a>, <a class="ref" href="jgraph_7.html#T43" target="_self">Th43</a>, <a class="ref" href="jgraph_7.html#T44" target="_self">Th44</a></i>;<br/>
<b>reconsider </b><font color="Maroon">f2</font> = <span class="p1">(<span class="default"><a href="jgraph_2.html#K2">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"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">a</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"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c</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> 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/>
<b>reconsider </b><font color="Maroon">g2</font> = <span class="p1">(<span class="default"><a href="jgraph_2.html#K2">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"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">a</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"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c</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/>
<b>reconsider </b><font color="Maroon">O</font> = 0, <font color="Maroon">I</font> = 1 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="rcomp_1.html#T48">RCOMP_1:48</a>, <a class="ref" href="borsuk_1.html#T83">BORSUK_1:83</a></i>;<br/>
<a NAME="E12:104"/><i><font color="Green">E105</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="E13:104"/><i><font color="Green">E106</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="E14:104"/><i><font color="Green">E109</font></i>: 
<span class="p1">(<span class="default"><a href="jgraph_2.html#K2">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"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">a</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"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c</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">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">I</font>
 
<b>by </b><i><a class="ref" href="jgraph_7.html#T42" target="_self">Th42</a>, <a class="ref" href="jgraph_7.html#T48" target="_self">Th48</a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>;<br/>
<a NAME="E15:104"/><i><font color="Green">E112</font></i>: 
<span class="p1">(<span class="default"><a href="jgraph_2.html#K2">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"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">a</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"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c</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">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">I</font>
 
<b>by </b><i><a class="ref" href="jgraph_7.html#T42" target="_self">Th42</a>, <a class="ref" href="jgraph_7.html#T49" target="_self">Th49</a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>;<br/>
<a NAME="E16:104"/><i><font color="Green">E113</font></i>: 
( <font color="Maroon">f2</font> is <a href="pre_topc.html#V5">continuous</a> &amp; <font color="Maroon">f2</font> is <a href="funct_1.html#V2">one-to-one</a> )
 
<b>by </b><i><a class="ref" href="jgraph_7.html#T42" target="_self">Th42</a>, <a class="ref" href="jgraph_7.html#T11" target="_self">Th11</a></i>;<br/>
<a NAME="E17:104"/><i><font color="Green">E114</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 &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="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1 )
 
<b>by </b><i><a class="ref" href="jgraph_7.html#T42" target="_self">Th42</a>, <a class="ref" href="jgraph_7.html#T12" target="_self">Th12</a>, </i>;<br/>
<a NAME="E18:104"/>
( <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#K22">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> )
 
<b>by </b><i><a class="ref" href="jgraph_7.html#T42" target="_self">Th42</a></i>;<br/>
<a NAME="E19:104"/><b>then </b><i><font color="Green">E115</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#NR3" target="_self">&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#K21">`1</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#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 )
 
<b>by </b><i><a class="ref" href="jgraph_7.html#T17" target="_self">Th17</a>, <a class="ref" href="jgraph_7.html#T42" target="_self">Th42</a>, <a class="ref" href="jgraph_7.html#T46" target="_self">Th46</a></i>;<br/>
<a NAME="E20:104"/><i><font color="Green">E116</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">f2</font> <a href="tarski.html#R1">c=</a>  <a href="jgraph_6.html#K2">closed_inside_of_rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1
 
<b>by </b><i><a class="ref" href="jgraph_7.html#T42" target="_self">Th42</a>, <a class="ref" href="jgraph_7.html#T10" target="_self">Th10</a></i>;<br/>
<a NAME="E21:104"/><i><font color="Green">E117</font></i>: 
( <font color="Maroon">g2</font> is <a href="pre_topc.html#V5">continuous</a> &amp; <font color="Maroon">g2</font> is <a href="funct_1.html#V2">one-to-one</a> )
 
<b>by </b><i><a class="ref" href="jgraph_7.html#T42" target="_self">Th42</a>, <a class="ref" href="jgraph_7.html#T11" target="_self">Th11</a></i>;<br/>
<a NAME="E22:104"/><i><font color="Green">E118</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> 1 &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#K22">`2</a>  <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1 )
 
<b>by </b><i><a class="ref" href="jgraph_7.html#T42" target="_self">Th42</a>, <a class="ref" href="jgraph_7.html#T14" target="_self">Th14</a>, </i>;<br/>
<a NAME="E23:104"/><i><font color="Green">E119</font></i>: 
( 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</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#K22">`2</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#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> 1 &amp; 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</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#NR4" target="_self">&gt;</a>  <a href="real_1.html#K1">-</a> 1 )
 
<b>by </b><i><a class="ref" href="jgraph_7.html#T22" target="_self">Th22</a>, <a class="ref" href="jgraph_7.html#T42" target="_self">Th42</a>, <a class="ref" href="jgraph_7.html#T45" target="_self">Th45</a></i>;<br/>
<a NAME="E24:104"/><i><font color="Green">E120</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">g2</font> <a href="tarski.html#R1">c=</a>  <a href="jgraph_6.html#K2">closed_inside_of_rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1
 
<b>by </b><i><a class="ref" href="jgraph_7.html#T42" target="_self">Th42</a>, <a class="ref" href="jgraph_7.html#T10" target="_self">Th10</a></i>;<br/>
<a NAME="E25:104"/><i><font color="Green">E151</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="xxreal_0.html#NR3" target="_self">&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#K21">`1</a> 
 
<b>by </b><i><a class="ref" href="jgraph_7.html#T47" target="_self">Th47</a>, <a class="ref" href="jgraph_7.html#T42" target="_self">Th42</a>, , </i>;<br/>
<a NAME="E26:104"/>
<font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font>,<font color="Maroon">g2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font>,<font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">I</font>,<font color="Maroon">g2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">I</font> <a href="jordan17.html#R1">are_in_this_order_on</a>  <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1
 
<b>by </b><i><a class="txt" href="jgraph_7.html#E5:104"><i><font color="Green">E32</font></i></a>, , , , , <a class="txt" href="jgraph_7.html#E12:104"><i><font color="Green">E105</font></i></a></i>;<br/>
<a NAME="E27:104"/><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="txt" href="jgraph_7.html#E8:104"><i><font color="Green">E100</font></i></a>, , , <a class="ref" href="jgraph_6.html#T89">JGRAPH_6:89</a></i>;<br/>
<a NAME="E28:104"/><b>then </b><i><font color="Green">E152</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">x</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="E30:104"/><i><font color="Green">E153</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>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">g2</font> )
 
<b>by </b><i><a class="txt" href="jgraph_7.html#E13:104"><i><font color="Green">E106</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>then consider </b><font color="Maroon">z1</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E32:104"/><i><font color="Green">E154</font></i>: 
( <font color="Maroon">z1</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">z1</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>consider </b><font color="Maroon">z2</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E34:104"/><i><font color="Green">E155</font></i>: 
( <font color="Maroon">z2</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">z2</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a>, </i>;<br/>
<a NAME="E35:104"/><i><font color="Green">E156</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="jgraph_2.html#K2">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"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">a</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"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c</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">z1</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a>, <a class="ref" href="jgraph_7.html#T48" target="_self">Th48</a></i>;<br/>
<a NAME="E36:104"/><i><font color="Green">E157</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="jgraph_2.html#K2">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"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">a</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"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c</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">z2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_7.html#E14:104"><i><font color="Green">E109</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a>, <a class="ref" href="jgraph_7.html#T49" target="_self">Th49</a></i>;<br/>
<a NAME="E37:104"/><i><font color="Green">E158</font></i>: 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z1</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_7.html#T48" target="_self">Th48</a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E38:104"/><i><font color="Green">E159</font></i>: 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z2</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="txt" href="jgraph_7.html#E14:104"><i><font color="Green">E109</font></i></a>, <a class="ref" href="jgraph_7.html#T49" target="_self">Th49</a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E39:104"/>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z1</font> <a href="hidden.html#R2">in</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#T7">FUNCT_2:7</a></i>;<br/>
<a NAME="E40:104"/><b>then </b><i><font color="Green">E160</font></i>: 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z1</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="jgraph_2.html#K2">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"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">a</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"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c</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>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E41:104"/>
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z2</font> <a href="hidden.html#R2">in</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="txt" href="jgraph_7.html#E14:104"><i><font color="Green">E109</font></i></a>, <a class="ref" href="funct_2.html#T7">FUNCT_2:7</a></i>;<br/>
<a NAME="E42:104"/><b>then </b><i><font color="Green">E161</font></i>: 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z2</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="jgraph_2.html#K2">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"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">a</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"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c</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>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E43:104"/>
 <a href="jgraph_2.html#K2">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"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K2">+</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></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"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K2">+</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></span>)</span> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i><a class="ref" href="jgraph_7.html#T47" target="_self">Th47</a>, <a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>;<br/>
<a NAME="E44:104"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z2</font>
 
<b>by </b><i><a class="txt" href="jgraph_7.html#E17:104"><i><font color="Green">E114</font></i></a>, <a class="txt" href="jgraph_7.html#E19:104"><i><font color="Green">E115</font></i></a>, , , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/>
<b>hence </b><a NAME="E45:104"/>
 <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="txt" href="jgraph_7.html#E15:104"><i><font color="Green">E112</font></i></a>, <a class="txt" href="jgraph_7.html#E16:104"><i><font color="Green">E113</font></i></a>, <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>


</div>
