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<b>assume </b><a NAME="E1:73_1_1"/><i><font color="Green" title="E41">A1</font></i>: 
( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">y</font> &amp; <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" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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/>

<b>then reconsider </b><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> <b>by </b><i><a class="ref" href="real_ns1.html#D6" title="REAL_NS1:def.6">REAL_NS1:def 6</a></i>;<br/>
<b>thus </b><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>
<b>by </b><i><a class="txt" href="#E1:73_1_1"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="real_ns1.html#D6" title="REAL_NS1:def.6">REAL_NS1:def 6</a></i>
<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>
<b>by </b><i><a class="ref" href="real_ns1.html#D2" title="REAL_NS1:def.2">REAL_NS1:def 2</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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