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

<b>let </b><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">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> holds   <a href="euclid_4.html#K1" title="EUCLID_4:func.1">Line</a> <font color="Olive" title="b1">x1</font>,<font color="Olive" title="b2">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="euclid_4.html#K1" title="EUCLID_4:func.1">Line</a> <font color="Olive" title="b2">x2</font>,<font color="Olive" title="b1">x1</font></span><br/><b>let </b><font color="Maroon" title="c2">x1</font>, <font color="Maroon" title="c3">x2</font> be    <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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="euclid_4.html#K1" title="EUCLID_4:func.1">Line</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="euclid_4.html#K1" title="EUCLID_4:func.1">Line</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font></span><br/>





<a NAME="E1:9"/>
(  <a href="euclid_4.html#K1" title="EUCLID_4:func.1">Line</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">x2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="euclid_4.html#K1" title="EUCLID_4:func.1">Line</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font> &amp;  <a href="euclid_4.html#K1" title="EUCLID_4:func.1">Line</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="euclid_4.html#K1" title="EUCLID_4:func.1">Line</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">x2</font> )
 
<b>by </b><i><a class="txt" href="euclid_4.html#E10"><i><font color="Green" title="E4">Lm1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:9"/>
 <a href="euclid_4.html#K1" title="EUCLID_4:func.1">Line</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="euclid_4.html#K1" title="EUCLID_4:func.1">Line</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
