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

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:69_1_1"/><span class="lab"><font color="Green" title="E36">A1</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">y</font>
 <span class="kw">and </span><br/><a NAME="E2:69_1_1"/><span class="lab"><font color="Green" title="E37">A2</font></span>: 
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> <a href="rvsum_1.html#NK11" title="RVSUM_1:NK.11">*</a> <font color="Maroon" title="c3">y</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c6">y1</font> = <font color="Maroon" title="c3">y</font> as    <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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="ref" href="real_ns1.html#D6" onmouseover="rs('real_ns1/D6')" onmouseout="rh()">REAL_NS1:def 6</a></span>;<br/>
<span class="kw">thus </span><font color="Maroon" title="c4">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">x</font> = 
<span class="p1">(<span class="default"><a href="real_ns1.html#K2" title="REAL_NS1:func.2">Euclid_mult</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c6">y1</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="txt" href="#E2:69_1_1"><span class="lab"><font color="Green" title="E37">A2</font></span></a>, <a class="ref" href="real_ns1.html#D6" onmouseover="rs('real_ns1/D6')" onmouseout="rh()">REAL_NS1:def 6</a></span>
<br/>.= 
<font color="Maroon" title="c5">b</font> <a href="valued_1.html#K24" title="VALUED_1:func.24">(#)</a> <font color="Maroon" title="c3">y</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="real_ns1.html#D2" onmouseover="rs('real_ns1/D2')" onmouseout="rh()">REAL_NS1:def 2</a></span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
