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

<b>let </b><font color="Maroon" title="c1">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">G</font>, <font color="Olive" title="b2">H</font> being   <a href="seqfunc.html#M1" title="SEQFUNC:mode.1">Functional_Sequence</a> of <font color="Maroon" title="c1">D</font>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  holds   <a href="seqfunc.html#K5" title="SEQFUNC:func.5">abs</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">G</font> <a href="seqfunc.html#K9" title="SEQFUNC:func.9">/</a> <font color="Olive" title="b2">H</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="seqfunc.html#K5" title="SEQFUNC:func.5">abs</a> <font color="Olive" title="b1">G</font></span>)</span> <a href="seqfunc.html#K9" title="SEQFUNC:func.9">/</a> <span class="p1">(<span class="default"><a href="seqfunc.html#K5" title="SEQFUNC:func.5">abs</a> <font color="Olive" title="b2">H</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">G</font>, <font color="Maroon" title="c3">H</font> be    <a href="seqfunc.html#M1" title="SEQFUNC:mode.1">Functional_Sequence</a> of <font color="Maroon" title="c1">D</font>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="seqfunc.html#K5" title="SEQFUNC:func.5">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">G</font> <a href="seqfunc.html#K9" title="SEQFUNC:func.9">/</a> <font color="Maroon" title="c3">H</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="seqfunc.html#K5" title="SEQFUNC:func.5">abs</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="seqfunc.html#K9" title="SEQFUNC:func.9">/</a> <span class="p1">(<span class="default"><a href="seqfunc.html#K5" title="SEQFUNC:func.5">abs</a> <font color="Maroon" title="c3">H</font></span>)</span></span><br/>





<b>thus </b> <a href="seqfunc.html#K5" title="SEQFUNC:func.5">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">G</font> <a href="seqfunc.html#K9" title="SEQFUNC:func.9">/</a> <font color="Maroon" title="c3">H</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="seqfunc.html#K5" title="SEQFUNC:func.5">abs</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="seqfunc.html#K8" title="SEQFUNC:func.8">(#)</a> <span class="p1">(<span class="default"><a href="seqfunc.html#K5" title="SEQFUNC:func.5">abs</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">H</font> <a href="seqfunc.html#K3" title="SEQFUNC:func.3">"</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seqfunc.html#T17" target="_self" title="SEQFUNC:th.17">Th17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="seqfunc.html#K5" title="SEQFUNC:func.5">abs</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="seqfunc.html#K9" title="SEQFUNC:func.9">/</a> <span class="p1">(<span class="default"><a href="seqfunc.html#K5" title="SEQFUNC:func.5">abs</a> <font color="Maroon" title="c3">H</font></span>)</span>
<b>by </b><i><a class="ref" href="seqfunc.html#T16" target="_self" title="SEQFUNC:th.16">Th16</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
