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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">G</font>, <font color="Olive" title="b2">H</font> being  <a href="seqfunc.html#NM1" title="SEQFUNC:NM.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="relset_1.html#R2" title="RELSET_1:pred.2">=</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/><span class="kw">let </span><font color="Maroon" title="c2">G</font>, <font color="Maroon" title="c3">H</font> be   <a href="seqfunc.html#NM1" title="SEQFUNC:NM.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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="relset_1.html#R2" title="RELSET_1:pred.2">=</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/>





<span class="kw">thus </span> <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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="seqfunc.html#T17" target="_self" title="SEQFUNC:th.17">Th17</a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="seqfunc.html#T16" target="_self" title="SEQFUNC:th.16">Th16</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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