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

<a NAME="E1:70_1_1"/>
 ex <font color="Olive" title="b1">a01</font>, <font color="Olive" title="b2">a02</font>, <font color="Olive" title="b3">a03</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> st <br/>( <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">a01</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">p1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">a02</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">a03</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">p3</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">a01</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Olive" title="b2">a02</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Olive" title="b3">a03</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; ( for <font color="Olive" title="b4">b1</font>, <font color="Olive" title="b5">b2</font>, <font color="Olive" title="b6">b3</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b4">b1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">p1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b5">b2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b6">b3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">p3</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b4">b1</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Olive" title="b5">b2</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Olive" title="b6">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 holds <br/>( <font color="Olive" title="b4">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a01</font> &amp; <font color="Olive" title="b5">b2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a02</font> &amp; <font color="Olive" title="b6">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">a03</font> ) ) )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:70"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="ref" href="euclid_3.html#T60" target="_self" title="EUCLID_3:th.60">Th60</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:70_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive" title="b2">a2</font>, <font color="Olive" title="b3">a3</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> st <br/>( <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Olive" title="b2">a2</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Olive" title="b3">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">p1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">p3</font></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
