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

<span class="kw">let </span><font color="Maroon" title="c1">seq</font>, <font color="Maroon" title="c2">seq1</font> be   <a href="comseq_1.html#NM1" title="COMSEQ_1:NM.1">Complex_Sequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">seq</font> is  <a href="comseq_1.html#NV1" title="COMSEQ_1:NV.1">non-zero</a>  implies (  <a href="valued_1.html#K31" title="VALUED_1:func.31">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">seq1</font> <a href="valued_1.html#K51" title="VALUED_1:func.51">/"</a> <font color="Maroon" title="c1">seq</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="valued_1.html#K31" title="VALUED_1:func.31">-</a> <font color="Maroon" title="c2">seq1</font></span>)</span> <a href="valued_1.html#K51" title="VALUED_1:func.51">/"</a> <font color="Maroon" title="c1">seq</font> &amp; <font color="Maroon" title="c2">seq1</font> <a href="valued_1.html#K51" title="VALUED_1:func.51">/"</a> <span class="p1">(<span class="default"><a href="valued_1.html#K31" title="VALUED_1:func.31">-</a> <font color="Maroon" title="c1">seq</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="valued_1.html#K31" title="VALUED_1:func.31">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">seq1</font> <a href="valued_1.html#K51" title="VALUED_1:func.51">/"</a> <font color="Maroon" title="c1">seq</font></span>)</span> ) )</span><br/>



<span class="kw">assume </span><a NAME="E1:43"/><span class="lab"><font color="Green" title="E22">A1</font></span>: 
<font color="Maroon" title="c1">seq</font> is  <a href="comseq_1.html#NV1" title="COMSEQ_1:NV.1">non-zero</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="valued_1.html#K31" title="VALUED_1:func.31">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">seq1</font> <a href="valued_1.html#K51" title="VALUED_1:func.51">/"</a> <font color="Maroon" title="c1">seq</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="valued_1.html#K31" title="VALUED_1:func.31">-</a> <font color="Maroon" title="c2">seq1</font></span>)</span> <a href="valued_1.html#K51" title="VALUED_1:func.51">/"</a> <font color="Maroon" title="c1">seq</font> &amp; <font color="Maroon" title="c2">seq1</font> <a href="valued_1.html#K51" title="VALUED_1:func.51">/"</a> <span class="p1">(<span class="default"><a href="valued_1.html#K31" title="VALUED_1:func.31">-</a> <font color="Maroon" title="c1">seq</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="valued_1.html#K31" title="VALUED_1:func.31">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">seq1</font> <a href="valued_1.html#K51" title="VALUED_1:func.51">/"</a> <font color="Maroon" title="c1">seq</font></span>)</span> )</span><br/>

<span class="kw">thus </span> <a href="valued_1.html#K31" title="VALUED_1:func.31">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">seq1</font> <a href="valued_1.html#K51" title="VALUED_1:func.51">/"</a> <font color="Maroon" title="c1">seq</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> </span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">seq1</font> <a href="valued_1.html#K51" title="VALUED_1:func.51">/"</a> <font color="Maroon" title="c1">seq</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> </span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <font color="Maroon" title="c2">seq1</font></span>)</span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K36" title="VALUED_1:func.36">"</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="comseq_1.html#T15" target="_self" title="COMSEQ_1:th.15">Th15</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="valued_1.html#K31" title="VALUED_1:func.31">-</a> <font color="Maroon" title="c2">seq1</font></span>)</span> <a href="valued_1.html#K51" title="VALUED_1:func.51">/"</a> <font color="Maroon" title="c1">seq</font>

; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">seq1</font> <a href="valued_1.html#K51" title="VALUED_1:func.51">/"</a> <span class="p1">(<span class="default"><a href="valued_1.html#K31" title="VALUED_1:func.31">-</a> <font color="Maroon" title="c1">seq</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="valued_1.html#K31" title="VALUED_1:func.31">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">seq1</font> <a href="valued_1.html#K51" title="VALUED_1:func.51">/"</a> <font color="Maroon" title="c1">seq</font></span>)</span></span><br/>

<span class="kw">thus </span><font color="Maroon" title="c2">seq1</font> <a href="valued_1.html#K51" title="VALUED_1:func.51">/"</a> <span class="p1">(<span class="default"><a href="valued_1.html#K31" title="VALUED_1:func.31">-</a> <font color="Maroon" title="c1">seq</font></span>)</span> = 
<font color="Maroon" title="c2">seq1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> </span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K36" title="VALUED_1:func.36">"</a> </span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43"><span class="lab"><font color="Green" title="E22">A1</font></span></a>, <a class="ref" href="comseq_1.html#T44" target="_self" title="COMSEQ_1:th.44">Th44</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> </span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">seq1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K36" title="VALUED_1:func.36">"</a> </span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="comseq_1.html#T16" target="_self" title="COMSEQ_1:th.16">Th16</a></span>
<br/>.= 
 <a href="valued_1.html#K31" title="VALUED_1:func.31">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">seq1</font> <a href="valued_1.html#K51" title="VALUED_1:func.51">/"</a> <font color="Maroon" title="c1">seq</font></span>)</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/>


</div>
