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<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>
 
<span class="kw">by</span> <span class="lab"><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">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">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> <span class="kw">by</span> <span class="lab"><a class="ref" href="real_ns1.html#D4" onmouseover="rs('real_ns1/D4')" onmouseout="rh()">REAL_NS1:def 4</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:70_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">a</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">  <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/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">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> <span class="kw">by</span> <span class="lab"><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> <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="c4">xn</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="real_ns1.html#T13" onmouseover="rs('real_ns1/T13')" onmouseout="rh()">REAL_NS1:13</a></span>
<br/>.= 
 <a href="euclid.html#K6" title="EUCLID:func.6">-</a> <font color="Maroon" title="c5">a1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:70_1_1"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="ref" href="real_ns1.html#T4" onmouseover="rs('real_ns1/T4')" onmouseout="rh()">REAL_NS1:4</a></span>
<br/>.= 
 <a href="valued_1.html#K30" title="VALUED_1:func.30">-</a> <font color="Maroon" title="c3">a</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"> verum</span><br/>


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