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

<b>let </b><font color="Maroon">S</font> be   <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>, <font color="Maroon">T</font> be   <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>;<br/>

<b>assume </b><a NAME="E1:13"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">S</font> <a href="hidden.html#R1">=</a> <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="Olive">p</font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Olive">p</font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> </span>}</span>  &amp; <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> <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="Olive">p</font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Olive">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> </span>}</span>  )
 ;<br/>

<b>set </b><font color="Maroon">A</font> = 1;<br/>
<b>set </b><font color="Maroon">B</font> = 0;<br/>
<b>set </b><font color="Maroon">C</font> = 1 <a href="real_1.html#K6">/</a> 2;<br/>
<b>set </b><font color="Maroon">D</font> =  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>;<br/>
<b>set </b><font color="Maroon">f</font> =  <a href="jgraph_2.html#K2">AffineMap</a> 1,0,<span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span>;<br/>
<a NAME="E2:13"/>
<span class="p1">(<span class="default"><a href="jgraph_2.html#K2">AffineMap</a> 1,0,<span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">S</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:13_1"/>
<span class="p1">(<span class="default"><a href="jgraph_2.html#K2">AffineMap</a> 1,0,<span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">S</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">T</font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:13_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="jgraph_2.html#K2">AffineMap</a> 1,0,<span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">S</font>
 ;<br/>

<b>then consider </b><font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:13_1_1"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">y</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> 1,0,<span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span>)</span> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> &amp; <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> 1,0,<span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D12">FUNCT_1:def 12</a></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="E5:13_1_1"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> &amp; <font color="Maroon">p</font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> )
 <b>by </b><i>, </i>;<br/>
<b>set </b><font color="Maroon">b</font> = <span class="p1">(<span class="default"><a href="jgraph_2.html#K2">AffineMap</a> 1,0,<span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">p</font>;<br/>
<a NAME="E6:13_1_1"/><i><font color="Green">E35</font></i>: 
<span class="p1">(<span class="default"><a href="jgraph_2.html#K2">AffineMap</a> 1,0,<span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">p</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">1 <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K3">+</a> 0</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
 
<b>by </b><i><a class="ref" href="jgraph_2.html#D2">JGRAPH_2:def 2</a></i>;<br/>
<a NAME="E7:13_1_1"/><b>then </b><i><font color="Green">E36</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jgraph_2.html#K2">AffineMap</a> 1,0,<span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">p</font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K3">+</a> 0
 
<b>by </b><i><a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/>
<a NAME="E8:13_1_1"/>
<span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/>
<a NAME="E9:13_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E10:13_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jgraph_2.html#K2">AffineMap</a> 1,0,<span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">p</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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jgraph_2.html#K2">AffineMap</a> 1,0,<span class="p4">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">p</font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span>
 
<b>by </b><i>, , <a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/>
<b>hence </b><a NAME="E11:13_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font>
 <b>by </b><i>, , </i>;<br/>


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

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

<b>assume </b><a NAME="E2:13_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font>
 ;<br/>

<b>then 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="E4:13_1"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> &amp; <font color="Maroon">p</font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> )
 <b>by </b><i/>;<br/>
<a NAME="E5:13_1"/>
 <a href="jgraph_2.html#K2">AffineMap</a> 1,0,<span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span> is <a href="funct_2.html#V2">onto</a>
 
<b>by </b><i><a class="ref" href="jordan1k.html#T36">JORDAN1K:36</a></i>;<br/>
<a NAME="E6:13_1"/><b>then </b>
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="jgraph_2.html#K2">AffineMap</a> 1,0,<span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</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#D3">FUNCT_2:def 3</a></i>;<br/>
<b>then consider </b><font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E8:13_1"/><i><font color="Green">E62</font></i>: 
( <font color="Maroon">y</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> 1,0,<span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span>)</span> &amp; <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> 1,0,<span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</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">y</font> = <font color="Maroon">y</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>set </b><font color="Maroon">b</font> = <span class="p1">(<span class="default"><a href="jgraph_2.html#K2">AffineMap</a> 1,0,<span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>;<br/>
<a NAME="E10:13_1"/><i><font color="Green">E63</font></i>: 
<span class="p1">(<span class="default"><a href="jgraph_2.html#K2">AffineMap</a> 1,0,<span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</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">1 <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K3">+</a> 0</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
 
<b>by </b><i><a class="ref" href="jgraph_2.html#D2">JGRAPH_2:def 2</a></i>;<br/>
<a NAME="E11:13_1"/><b>then </b><i><font color="Green">E64</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jgraph_2.html#K2">AffineMap</a> 1,0,<span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> <a href="euclid.html#K21">`1</a> 
 
<b>by </b><i><a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/>
<a NAME="E12:13_1"/><i><font color="Green">E65</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jgraph_2.html#K2">AffineMap</a> 1,0,<span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</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">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/>
<a NAME="E13:13_1"/>
2 <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jgraph_2.html#K2">AffineMap</a> 1,0,<span class="p4">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 2 <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span>
 
<b>by </b><i>, , , <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/>
<a NAME="E14:13_1"/><b>then </b>
<span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jgraph_2.html#K2">AffineMap</a> 1,0,<span class="p5">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p0">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K3">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E15:13_1"/><b>then </b>
<font color="Maroon">y</font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E16:13_1"/><b>then </b>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E17:13_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="jgraph_2.html#K2">AffineMap</a> 1,0,<span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">S</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#D12">FUNCT_1:def 12</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:13"/>
<span class="p1">(<span class="default"><a href="jgraph_2.html#K2">AffineMap</a> 1,0,<span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">S</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 ;<br/>


</div>
