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<b>let </b><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="euclid.html#K10" title="EUCLID:func.10">abs</a> <span class="p1">(<span class="default"><a href="jordan2c.html#K4" title="JORDAN2C:func.4">1*</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> <a href="finseq_2.html#K2" title="FINSEQ_2:func.2">|-&gt;</a> 1</span><br/>

<b>thus </b> <a href="euclid.html#K10" title="EUCLID:func.10">abs</a> <span class="p1">(<span class="default"><a href="jordan2c.html#K4" title="JORDAN2C:func.4">1*</a> <font color="Maroon" title="c1">n</font></span>)</span> = 
<font color="Maroon" title="c1">n</font> <a href="finseq_2.html#K2" title="FINSEQ_2:func.2">|-&gt;</a> <span class="p1">(<span class="default"><a href="euclid.html#K2" title="EUCLID:func.2">absreal</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="finseqop.html#T17" title="FINSEQOP:th.17">FINSEQOP:17</a></i>
<br/>.= 
<font color="Maroon" title="c1">n</font> <a href="finseq_2.html#K2" title="FINSEQ_2:func.2">|-&gt;</a> <span class="p1">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#D2" title="EUCLID:def.2">EUCLID:def 2</a></i>
<br/>.= 
<font color="Maroon" title="c1">n</font> <a href="finseq_2.html#K2" title="FINSEQ_2:func.2">|-&gt;</a> 1
<b>by </b><i><a class="ref" href="absvalue.html#D1" title="ABSVALUE:def.1">ABSVALUE:def 1</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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