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<b>let </b><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">L0</font>, <font color="Maroon" title="c3">L1</font>, <font color="Maroon" title="c4">L2</font>, <font color="Maroon" title="c5">L</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="euclidlp.html#K1" title="EUCLIDLP:func.1">line_of_REAL</a> <font color="Maroon" title="c1">n</font>;<br/><b>let </b><font color="Maroon" title="c6">P</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="euclidlp.html#K5" title="EUCLIDLP:func.5">plane_of_REAL</a> <font color="Maroon" title="c1">n</font>;<br/>











<b>assume </b><a NAME="E1:126"/><i><font color="Green" title="E104">A1</font></i>: 
( <font color="Maroon" title="c2">L0</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">P</font> &amp; <font color="Maroon" title="c3">L1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">P</font> &amp; <font color="Maroon" title="c4">L2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">P</font> &amp; <font color="Maroon" title="c2">L0</font> <a href="euclidlp.html#R5" title="EUCLIDLP:pred.5">//</a> <font color="Maroon" title="c3">L1</font> &amp; <font color="Maroon" title="c3">L1</font> <a href="euclidlp.html#R5" title="EUCLIDLP:pred.5">//</a> <font color="Maroon" title="c4">L2</font> &amp; <font color="Maroon" title="c2">L0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">L1</font> &amp; <font color="Maroon" title="c3">L1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">L2</font> &amp; <font color="Maroon" title="c4">L2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">L0</font> )
 ;<br/>

<a NAME="E2:126"/><b>then </b><i><font color="Green" title="E105">A2</font></i>: 
<font color="Maroon" title="c2">L0</font> <a href="euclidlp.html#R5" title="EUCLIDLP:pred.5">//</a> <font color="Maroon" title="c4">L2</font>
 
<b>by </b><i><a class="ref" href="euclidlp.html#T65" target="_self" title="EUCLIDLP:th.65">Th65</a></i>;<br/>
<a NAME="E3:126"/><i><font color="Green" title="E106">A3</font></i>: 
( <font color="Maroon" title="c2">L0</font> <a href="euclid_4.html#NR1" title="EUCLID_4:NR.1">is_line</a>  &amp; <font color="Maroon" title="c3">L1</font> <a href="euclid_4.html#NR1" title="EUCLID_4:NR.1">is_line</a>  &amp; <font color="Maroon" title="c4">L2</font> <a href="euclid_4.html#NR1" title="EUCLID_4:NR.1">is_line</a>  )
 
<b>by </b><i><a class="txt" href="euclidlp.html#E1:126"><i><font color="Green" title="E104">A1</font></i></a>, <a class="ref" href="euclidlp.html#T71" target="_self" title="EUCLIDLP:th.71">Th71</a></i>;<br/>
<b>assume </b><a NAME="E4:126"/><i><font color="Green" title="E107">A4</font></i>: 
( <font color="Maroon" title="c5">L</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c2">L0</font> &amp; <font color="Maroon" title="c5">L</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c3">L1</font> )
 ;<br/>

<b>then consider </b><font color="Maroon" title="c7">x0</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c1">n</font><b> such that </b><br/><a NAME="E6:126"/><i><font color="Green" title="E108">A5</font></i>: 
( <font color="Maroon" title="c7">x0</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">L</font> &amp; <font color="Maroon" title="c7">x0</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">L0</font> )
 <b>by </b><i><a class="ref" href="euclidlp.html#T54" target="_self" title="EUCLIDLP:th.54">Th54</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c8">x1</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c1">n</font><b> such that </b><br/><a NAME="E8:126"/><i><font color="Green" title="E109">A6</font></i>: 
( <font color="Maroon" title="c8">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">L</font> &amp; <font color="Maroon" title="c8">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">L1</font> )
 <b>by </b><i><a class="txt" href="euclidlp.html#E4:126"><i><font color="Green" title="E107">A4</font></i></a>, <a class="ref" href="euclidlp.html#T54" target="_self" title="EUCLIDLP:th.54">Th54</a></i>;<br/>
<a NAME="E9:126"/><i><font color="Green" title="E110">A7</font></i>: 
( <font color="Maroon" title="c2">L0</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c3">L1</font> &amp; <font color="Maroon" title="c3">L1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c4">L2</font> &amp; <font color="Maroon" title="c2">L0</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c4">L2</font> )
 
<b>by </b><i><a class="txt" href="euclidlp.html#E1:126"><i><font color="Green" title="E104">A1</font></i></a>, <a class="txt" href="euclidlp.html#E2:126"><i><font color="Green" title="E105">A2</font></i></a>, <a class="ref" href="euclidlp.html#T76" target="_self" title="EUCLIDLP:th.76">Th76</a></i>;<br/>
<a NAME="E10:126"/><b>then </b><i><font color="Green" title="E111">A8</font></i>: 
( not <font color="Maroon" title="c7">x0</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">L1</font> &amp; not <font color="Maroon" title="c7">x0</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">L2</font> &amp; not <font color="Maroon" title="c8">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">L0</font> &amp; not <font color="Maroon" title="c8">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">L2</font> )
 
<b>by </b><i><a class="txt" href="euclidlp.html#E6:126"><i><font color="Green" title="E108">A5</font></i></a>, <a class="txt" href="euclidlp.html#E8:126"><i><font color="Green" title="E109">A6</font></i></a>, <a class="ref" href="euclidlp.html#T54" target="_self" title="EUCLIDLP:th.54">Th54</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c9">L'</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="euclidlp.html#K1" title="EUCLIDLP:func.1">line_of_REAL</a> <font color="Maroon" title="c1">n</font><b> such that </b><br/><a NAME="E12:126"/><i><font color="Green" title="E112">A9</font></i>: 
( <font color="Maroon" title="c7">x0</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">L'</font> &amp; <font color="Maroon" title="c9">L'</font> <a href="euclidlp.html#R6" title="EUCLIDLP:pred.6">_|_</a> <font color="Maroon" title="c3">L1</font> &amp; <font color="Maroon" title="c9">L'</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c3">L1</font> )
 <b>by </b><i><a class="txt" href="euclidlp.html#E3:126"><i><font color="Green" title="E106">A3</font></i></a>, <a class="txt" href="euclidlp.html#E10:126"><i><font color="Green" title="E111">A8</font></i></a>, <a class="ref" href="euclidlp.html#T67" target="_self" title="EUCLIDLP:th.67">Th67</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c10">y1</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c1">n</font><b> such that </b><br/><a NAME="E14:126"/><i><font color="Green" title="E113">A10</font></i>: 
( <font color="Maroon" title="c10">y1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">L'</font> &amp; <font color="Maroon" title="c10">y1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">L1</font> )
 <b>by </b><i><a class="txt" href="euclidlp.html#E12:126"><i><font color="Green" title="E112">A9</font></i></a>, <a class="ref" href="euclidlp.html#T54" target="_self" title="EUCLIDLP:th.54">Th54</a></i>;<br/>
<a NAME="E15:126"/><i><font color="Green" title="E114">A11</font></i>: 
<font color="Maroon" title="c9">L'</font> <a href="euclidlp.html#R6" title="EUCLIDLP:pred.6">_|_</a> <font color="Maroon" title="c4">L2</font>
 
<b>by </b><i><a class="txt" href="euclidlp.html#E12:126"><i><font color="Green" title="E112">A9</font></i></a>, <a class="txt" href="euclidlp.html#E1:126"><i><font color="Green" title="E104">A1</font></i></a>, <a class="ref" href="euclidlp.html#T66" target="_self" title="EUCLIDLP:th.66">Th66</a></i>;<br/>
<a NAME="E16:126"/><i><font color="Green" title="E115">A12</font></i>: 
<font color="Maroon" title="c7">x0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">y1</font>
 
<b>by </b><i><a class="txt" href="euclidlp.html#E6:126"><i><font color="Green" title="E108">A5</font></i></a>, <a class="txt" href="euclidlp.html#E9:126"><i><font color="Green" title="E110">A7</font></i></a>, <a class="txt" href="euclidlp.html#E14:126"><i><font color="Green" title="E113">A10</font></i></a>, <a class="ref" href="euclidlp.html#T54" target="_self" title="EUCLIDLP:th.54">Th54</a></i>;<br/>
<a NAME="E17:126"/><b>then </b><i><font color="Green" title="E116">A13</font></i>: 
( <font color="Maroon" title="c9">L'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="euclid_4.html#K2" title="EUCLID_4:func.2">Line</a> <font color="Maroon" title="c7">x0</font>,<font color="Maroon" title="c10">y1</font> &amp; <font color="Maroon" title="c9">L'</font> <a href="euclid_4.html#NR1" title="EUCLID_4:NR.1">is_line</a>  )
 
<b>by </b><i><a class="txt" href="euclidlp.html#E12:126"><i><font color="Green" title="E112">A9</font></i></a>, <a class="txt" href="euclidlp.html#E14:126"><i><font color="Green" title="E113">A10</font></i></a>, <a class="ref" href="euclidlp.html#T69" target="_self" title="EUCLIDLP:th.69">Th69</a></i>;<br/>
<a NAME="E18:126"/>
<font color="Maroon" title="c9">L'</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">P</font>
 
<b>by </b><i><a class="txt" href="euclidlp.html#E1:126"><i><font color="Green" title="E104">A1</font></i></a>, <a class="txt" href="euclidlp.html#E6:126"><i><font color="Green" title="E108">A5</font></i></a>, <a class="txt" href="euclidlp.html#E14:126"><i><font color="Green" title="E113">A10</font></i></a>, <a class="txt" href="euclidlp.html#E17:126"><i><font color="Green" title="E116">A13</font></i></a>, <a class="ref" href="euclidlp.html#T100" target="_self" title="EUCLIDLP:th.100">Th100</a></i>;<br/>
<a NAME="E19:126"/><b>then </b>
<font color="Maroon" title="c9">L'</font>,<font color="Maroon" title="c4">L2</font> <a href="euclidlp.html#R7" title="EUCLIDLP:pred.7">are_coplane</a> 
 
<b>by </b><i><a class="txt" href="euclidlp.html#E1:126"><i><font color="Green" title="E104">A1</font></i></a>, <a class="ref" href="euclidlp.html#T101" target="_self" title="EUCLIDLP:th.101">Th101</a></i>;<br/>
<a NAME="E20:126"/><b>then </b><i><font color="Green" title="E117">A14</font></i>: 
<font color="Maroon" title="c9">L'</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c4">L2</font>
 
<b>by </b><i><a class="txt" href="euclidlp.html#E15:126"><i><font color="Green" title="E114">A11</font></i></a>, <a class="ref" href="euclidlp.html#T114" target="_self" title="EUCLIDLP:th.114">Th114</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c11">y2</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c1">n</font><b> such that </b><br/><a NAME="E22:126"/><i><font color="Green" title="E118">A15</font></i>: 
( <font color="Maroon" title="c11">y2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">L'</font> &amp; <font color="Maroon" title="c11">y2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">L2</font> )
 <b>by </b><i><a class="ref" href="euclidlp.html#T54" target="_self" title="EUCLIDLP:th.54">Th54</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c12">x2</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c1">n</font><b> such that </b><br/><a NAME="E24:126"/><i><font color="Green" title="E119">A16</font></i>: 
( <font color="Maroon" title="c12">x2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">y2</font> &amp; <font color="Maroon" title="c12">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">L2</font> )
 <b>by </b><i><a class="txt" href="euclidlp.html#E3:126"><i><font color="Green" title="E106">A3</font></i></a>, <a class="txt" href="euclidlp.html#E22:126"><i><font color="Green" title="E118">A15</font></i></a>, <a class="ref" href="euclidlp.html#T58" target="_self" title="EUCLIDLP:th.58">Th58</a></i>;<br/>
<a NAME="E25:126"/><i><font color="Green" title="E120">A17</font></i>: 
<font color="Maroon" title="c4">L2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="euclid_4.html#K2" title="EUCLID_4:func.2">Line</a> <font color="Maroon" title="c11">y2</font>,<font color="Maroon" title="c12">x2</font>
 
<b>by </b><i><a class="txt" href="euclidlp.html#E24:126"><i><font color="Green" title="E119">A16</font></i></a>, <a class="txt" href="euclidlp.html#E22:126"><i><font color="Green" title="E118">A15</font></i></a>, <a class="ref" href="euclidlp.html#T69" target="_self" title="EUCLIDLP:th.69">Th69</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c13">a</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><br/><a NAME="E27:126"/><i><font color="Green" title="E121">A18</font></i>: 
<font color="Maroon" title="c11">y2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c7">x0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">a</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">y1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c7">x0</font></span>)</span>
 <b>by </b><i><a class="txt" href="euclidlp.html#E12:126"><i><font color="Green" title="E112">A9</font></i></a>, <a class="txt" href="euclidlp.html#E14:126"><i><font color="Green" title="E113">A10</font></i></a>, <a class="txt" href="euclidlp.html#E22:126"><i><font color="Green" title="E118">A15</font></i></a>, <a class="txt" href="euclidlp.html#E16:126"><i><font color="Green" title="E115">A12</font></i></a>, <a class="ref" href="euclidlp.html#T75" target="_self" title="EUCLIDLP:th.75">Th75</a></i>;<br/>
<a NAME="E28:126"/>
<font color="Maroon" title="c7">x0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">x1</font>
 
<b>by </b><i><a class="txt" href="euclidlp.html#E6:126"><i><font color="Green" title="E108">A5</font></i></a>, <a class="txt" href="euclidlp.html#E8:126"><i><font color="Green" title="E109">A6</font></i></a>, <a class="txt" href="euclidlp.html#E9:126"><i><font color="Green" title="E110">A7</font></i></a>, <a class="ref" href="euclidlp.html#T54" target="_self" title="EUCLIDLP:th.54">Th54</a></i>;<br/>
<a NAME="E29:126"/><b>then </b><i><font color="Green" title="E122">A19</font></i>: 
<font color="Maroon" title="c5">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="euclid_4.html#K2" title="EUCLID_4:func.2">Line</a> <font color="Maroon" title="c7">x0</font>,<font color="Maroon" title="c8">x1</font>
 
<b>by </b><i><a class="txt" href="euclidlp.html#E6:126"><i><font color="Green" title="E108">A5</font></i></a>, <a class="txt" href="euclidlp.html#E8:126"><i><font color="Green" title="E109">A6</font></i></a>, <a class="ref" href="euclidlp.html#T69" target="_self" title="EUCLIDLP:th.69">Th69</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="126_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:126_1_1"/>
( <font color="Maroon" title="c8">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">y1</font> or <font color="Maroon" title="c8">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">y1</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_1"><b>case </b></a><a NAME="E1:126_1_1_1"/>
<font color="Maroon" title="c8">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">y1</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:126_1_1_1"/>
<font color="Maroon" title="c5">L</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c4">L2</font>
 <b>by </b><i><a class="txt" href="euclidlp.html#E17:126"><i><font color="Green" title="E116">A13</font></i></a>, <a class="txt" href="euclidlp.html#E20:126"><i><font color="Green" title="E117">A14</font></i></a>, <a class="txt" href="euclidlp.html#E6:126"><i><font color="Green" title="E108">A5</font></i></a>, <a class="txt" href="euclidlp.html#E8:126"><i><font color="Green" title="E109">A6</font></i></a>, <a class="txt" href="euclidlp.html#E16:126"><i><font color="Green" title="E115">A12</font></i></a>, <a class="ref" href="euclidlp.html#T69" target="_self" title="EUCLIDLP:th.69">Th69</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_2"><b>case </b></a><a NAME="E1:126_1_1_2"/>
<font color="Maroon" title="c8">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">y1</font>
 ;<br/><div class="add"><a NAME="E2:126_1_1_2"/><b>then </b>
<font color="Maroon" title="c12">x2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c11">y2</font> <a href="euclidlp.html#R2" title="EUCLIDLP:pred.2">//</a> <font color="Maroon" title="c8">x1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c10">y1</font>
 <b>by </b><i><a class="txt" href="euclidlp.html#E8:126"><i><font color="Green" title="E109">A6</font></i></a>, <a class="txt" href="euclidlp.html#E14:126"><i><font color="Green" title="E113">A10</font></i></a>, <a class="txt" href="euclidlp.html#E24:126"><i><font color="Green" title="E119">A16</font></i></a>, <a class="txt" href="euclidlp.html#E22:126"><i><font color="Green" title="E118">A15</font></i></a>, <a class="txt" href="euclidlp.html#E1:126"><i><font color="Green" title="E104">A1</font></i></a>, <a class="ref" href="euclidlp.html#T82" target="_self" title="EUCLIDLP:th.82">Th82</a></i>;<br/><b>then consider </b><font color="Maroon" title="c14">b</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><br/><a NAME="E4:126_1_1_2"/><i><font color="Green" title="E123">A20</font></i>: 
( <font color="Maroon" title="c14">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0 &amp; <font color="Maroon" title="c12">x2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c11">y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">b</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">x1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c10">y1</font></span>)</span> )
 <b>by </b><i><a class="ref" href="euclidlp.html#T37" target="_self" title="EUCLIDLP:th.37">Th37</a></i>;<br/><i><font color="Green" title="E124">A21</font></i>: <font color="Maroon" title="c8">x1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c10">y1</font> = 
1 <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">x1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c10">y1</font></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T3" title="EUCLID_4:th.3">EUCLID_4:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c14">b</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c14">b</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">x1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c10">y1</font></span>)</span>
<b>by </b><i><a class="txt" href="euclidlp.html#E4:126_1_1_2"><i><font color="Green" title="E123">A20</font></i></a>, <a class="ref" href="xcmplx_1.html#T88" title="XCMPLX_1:th.88">XCMPLX_1:88</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c14">b</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">x2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c11">y2</font></span>)</span>
<b>by </b><i><a class="txt" href="euclidlp.html#E4:126_1_1_2"><i><font color="Green" title="E123">A20</font></i></a>, <a class="ref" href="euclid_4.html#T4" title="EUCLID_4:th.4">EUCLID_4:4</a></i>
;<br/><b>set </b><font color="Maroon" title="c15">x</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c13">a</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c7">x0</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c8">x1</font></span>)</span>;<br/><a NAME="E6:126_1_1_2"/><i><font color="Green" title="E125">A22</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c13">a</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c7">x0</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c8">x1</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">L</font>
 <b>by </b><i><a class="txt" href="euclidlp.html#E29:126"><i><font color="Green" title="E122">A19</font></i></a></i>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c13">a</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c7">x0</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c8">x1</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c7">x0</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c7">x0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c8">x1</font></span>)</span>
<b>by </b><i><a class="ref" href="euclidlp.html#T16" target="_self" title="EUCLIDLP:th.16">Th16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">x0</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c7">x0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c8">x1</font></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T3" title="EUCLID_4:th.3">EUCLID_4:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c8">x1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c7">x0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Maroon" title="c7">x0</font>
<b>by </b><i><a class="txt" href="euclidlp.html#E2"><i><font color="Green" title="E2">Lm1</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">x1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c7">x0</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Maroon" title="c7">x0</font>
<b>by </b><i><a class="ref" href="euclidlp.html#T17" target="_self" title="EUCLIDLP:th.17">Th17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">x1</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p3">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <font color="Maroon" title="c7">x0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Maroon" title="c7">x0</font>
<b>by </b><i><a class="txt" href="euclidlp.html#E6"><i><font color="Green" title="E6">Lm5</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">x1</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p4">(<span class="default"><a href="euclid.html#K5" title="EUCLID:func.5">0*</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p3">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <font color="Maroon" title="c7">x0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Maroon" title="c7">x0</font>
<b>by </b><i><a class="ref" href="euclid_4.html#T1" title="EUCLID_4:th.1">EUCLID_4:1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">x1</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <font color="Maroon" title="c10">y1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Maroon" title="c10">y1</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p3">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <font color="Maroon" title="c7">x0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Maroon" title="c7">x0</font>
<b>by </b><i><a class="ref" href="euclidlp.html#T7" target="_self" title="EUCLIDLP:th.7">Th7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">x1</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p5">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <font color="Maroon" title="c10">y1</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Maroon" title="c10">y1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p3">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <font color="Maroon" title="c7">x0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Maroon" title="c7">x0</font>
<b>by </b><i><a class="txt" href="euclidlp.html#E2"><i><font color="Green" title="E2">Lm1</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">x1</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p4">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <font color="Maroon" title="c10">y1</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">y1</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p4">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <font color="Maroon" title="c7">x0</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Maroon" title="c7">x0</font>
<b>by </b><i><a class="txt" href="euclidlp.html#E2"><i><font color="Green" title="E2">Lm1</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">x1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c10">y1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">y1</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p4">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <font color="Maroon" title="c7">x0</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Maroon" title="c7">x0</font>
<b>by </b><i><a class="txt" href="euclidlp.html#E6"><i><font color="Green" title="E6">Lm5</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">x1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c10">y1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">y1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c7">x0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Maroon" title="c7">x0</font>
<b>by </b><i><a class="txt" href="euclidlp.html#E6"><i><font color="Green" title="E6">Lm5</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c14">b</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">x2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c11">y2</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">y1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c7">x0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Maroon" title="c7">x0</font>
<b>by </b><i><a class="txt" href="euclidlp.html#E5:126_1_1_2"><i><font color="Green" title="E124">A21</font></i></a>, <a class="ref" href="euclid_4.html#T6" title="EUCLID_4:th.6">EUCLID_4:6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c14">b</font></span>)</span></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">x2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c11">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">y1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c7">x0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Maroon" title="c7">x0</font>
<b>by </b><i><a class="ref" href="euclid_4.html#T4" title="EUCLID_4:th.4">EUCLID_4:4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c14">b</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">x2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c11">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">y1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c7">x0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Maroon" title="c7">x0</font>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T100" title="XCMPLX_1:th.100">XCMPLX_1:100</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c14">b</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">x2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c11">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">y2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c7">x0</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Maroon" title="c7">x0</font></span>)</span>
<b>by </b><i><a class="txt" href="euclidlp.html#E2"><i><font color="Green" title="E2">Lm1</font></i></a>, <a class="txt" href="euclidlp.html#E27:126"><i><font color="Green" title="E121">A18</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c14">b</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">x2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c11">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">y2</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p3">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <font color="Maroon" title="c7">x0</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Maroon" title="c7">x0</font></span>)</span>
<b>by </b><i><a class="txt" href="euclidlp.html#E6"><i><font color="Green" title="E6">Lm5</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c14">b</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">x2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c11">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">y2</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <font color="Maroon" title="c7">x0</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Maroon" title="c7">x0</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="euclidlp.html#E2"><i><font color="Green" title="E2">Lm1</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c14">b</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">x2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c11">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">y2</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K5" title="EUCLID:func.5">0*</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclidlp.html#T7" target="_self" title="EUCLIDLP:th.7">Th7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c14">b</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">x2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c11">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Maroon" title="c11">y2</font>
<b>by </b><i><a class="ref" href="euclid_4.html#T1" title="EUCLID_4:th.1">EUCLID_4:1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c14">b</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c12">x2</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c14">b</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c11">y2</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Maroon" title="c11">y2</font>
<b>by </b><i><a class="ref" href="euclidlp.html#T17" target="_self" title="EUCLIDLP:th.17">Th17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c11">y2</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c14">b</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c11">y2</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c14">b</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c12">x2</font></span>)</span>
<b>by </b><i><a class="txt" href="euclidlp.html#E2"><i><font color="Green" title="E2">Lm1</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c11">y2</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c14">b</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c11">y2</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c14">b</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c12">x2</font></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T3" title="EUCLID_4:th.3">EUCLID_4:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c14">b</font></span>)</span></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c11">y2</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c14">b</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c12">x2</font></span>)</span>
<b>by </b><i><a class="ref" href="euclidlp.html#T16" target="_self" title="EUCLIDLP:th.16">Th16</a></i>
;<br/><a NAME="E8:126_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c13">a</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c7">x0</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c8">x1</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">L2</font>
 <b>by </b><i><a class="txt" href="euclidlp.html#E25:126"><i><font color="Green" title="E120">A17</font></i></a></i>;<br/><b>hence </b><a NAME="E9:126_1_1_2"/>
<font color="Maroon" title="c5">L</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c4">L2</font>
 <b>by </b><i><a class="txt" href="euclidlp.html#E6:126_1_1_2"><i><font color="Green" title="E125">A22</font></i></a>, <a class="ref" href="euclidlp.html#T54" target="_self" title="EUCLIDLP:th.54">Th54</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E31:126"/>
<font color="Maroon" title="c5">L</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c4">L2</font>
 ;<br/>


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