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<b>assume </b><a NAME="E1:74_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">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="valued_1.html#K30" title="VALUED_1:func.30">-</a> <font color="Maroon" title="c3">a</font></span><br/>

<b>then reconsider </b><font color="Maroon" title="c4">a1</font> = <font color="Maroon" title="c3">a</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/>
<a NAME="E3:74_1_1"/>
<font color="Maroon" title="c2">x</font> is    <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>then reconsider </b><font color="Maroon" title="c5">xn</font> = <font color="Maroon" title="c2">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="real_ns1.html#K4" title="REAL_NS1:func.4">REAL-NS</a> <font color="Maroon" title="c1">n</font></span>)</span> <b>by </b><i><a class="ref" href="real_ns1.html#D4" title="REAL_NS1:def.4">REAL_NS1:def 4</a></i>;<br/>
<b>thus </b> <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c2">x</font> = 
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">xn</font>
<b>by </b><i><a class="ref" href="real_ns1.html#T13" title="REAL_NS1:th.13">REAL_NS1:13</a></i>
<br/>.= 
 <a href="euclid.html#K6" title="EUCLID:func.6">-</a> <font color="Maroon" title="c4">a1</font>
<b>by </b><i><a class="txt" href="#E1:74_1_1"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="real_ns1.html#T4" title="REAL_NS1:th.4">REAL_NS1:4</a></i>
<br/>.= 
 <a href="valued_1.html#K30" title="VALUED_1:func.30">-</a> <font color="Maroon" title="c3">a</font>

; <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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