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<b>let </b><font color="Maroon" title="c1">seq</font>, <font color="Maroon" title="c2">seq'</font>, <font color="Maroon" title="c3">seq1</font>, <font color="Maroon" title="c4">seq1'</font> be   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">seq</font> is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-zero</a> &amp; <font color="Maroon" title="c2">seq'</font> is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-zero</a> implies ( <span class="p1">(<span class="default"><font color="Maroon" title="c3">seq1</font> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <font color="Maroon" title="c1">seq</font></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">seq1'</font> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <font color="Maroon" title="c2">seq'</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">seq1</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">seq'</font></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">seq1'</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">seq</font></span>)</span></span>)</span> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">seq'</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">seq1</font> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <font color="Maroon" title="c1">seq</font></span>)</span> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">seq1'</font> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <font color="Maroon" title="c2">seq'</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">seq1</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">seq'</font></span>)</span> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">seq1'</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">seq</font></span>)</span></span>)</span> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">seq'</font></span>)</span> ) )</span><br/>







<b>assume </b><b>that </b><br/><a NAME="E1:47"/><i><font color="Green" title="E26">A1</font></i>: 
<font color="Maroon" title="c1">seq</font> is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-zero</a>
 <b>and </b><br/><a NAME="E2:47"/><i><font color="Green" title="E27">A2</font></i>: 
<font color="Maroon" title="c2">seq'</font> is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-zero</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><font color="Maroon" title="c3">seq1</font> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <font color="Maroon" title="c1">seq</font></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">seq1'</font> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <font color="Maroon" title="c2">seq'</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">seq1</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">seq'</font></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">seq1'</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">seq</font></span>)</span></span>)</span> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">seq'</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">seq1</font> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <font color="Maroon" title="c1">seq</font></span>)</span> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">seq1'</font> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <font color="Maroon" title="c2">seq'</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">seq1</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">seq'</font></span>)</span> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">seq1'</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">seq</font></span>)</span></span>)</span> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">seq'</font></span>)</span> )</span><br/>

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c3">seq1</font> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <font color="Maroon" title="c1">seq</font></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">seq1'</font> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <font color="Maroon" title="c2">seq'</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">seq1</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">seq'</font></span>)</span> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">seq'</font></span>)</span></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">seq1'</font> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <font color="Maroon" title="c2">seq'</font></span>)</span>
<b>by </b><i><a class="txt" href="#E2:47"><i><font color="Green" title="E27">A2</font></i></a>, <a class="ref" href="seq_1.html#T51" target="_self" title="SEQ_1:th.51">Th51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">seq1</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">seq'</font></span>)</span> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">seq'</font></span>)</span></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">seq1'</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">seq</font></span>)</span> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">seq'</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:47"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="seq_1.html#T51" target="_self" title="SEQ_1:th.51">Th51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">seq1</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">seq'</font></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">seq1'</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">seq</font></span>)</span></span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">seq'</font></span>)</span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T23" target="_self" title="SEQ_1:th.23">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">seq1</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">seq'</font></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">seq1'</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">seq</font></span>)</span></span>)</span> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">seq'</font></span>)</span>

; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">seq1</font> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <font color="Maroon" title="c1">seq</font></span>)</span> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">seq1'</font> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <font color="Maroon" title="c2">seq'</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">seq1</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">seq'</font></span>)</span> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">seq1'</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">seq</font></span>)</span></span>)</span> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">seq'</font></span>)</span></span><br/>

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c3">seq1</font> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <font color="Maroon" title="c1">seq</font></span>)</span> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">seq1'</font> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <font color="Maroon" title="c2">seq'</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">seq1</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">seq'</font></span>)</span> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">seq'</font></span>)</span></span>)</span> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">seq1'</font> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <font color="Maroon" title="c2">seq'</font></span>)</span>
<b>by </b><i><a class="txt" href="#E2:47"><i><font color="Green" title="E27">A2</font></i></a>, <a class="ref" href="seq_1.html#T51" target="_self" title="SEQ_1:th.51">Th51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">seq1</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">seq'</font></span>)</span> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">seq'</font></span>)</span></span>)</span> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">seq1'</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">seq</font></span>)</span> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">seq'</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:47"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="seq_1.html#T51" target="_self" title="SEQ_1:th.51">Th51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">seq1</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">seq'</font></span>)</span> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">seq1'</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">seq</font></span>)</span></span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">seq'</font></span>)</span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T28" target="_self" title="SEQ_1:th.28">Th28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">seq1</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">seq'</font></span>)</span> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">seq1'</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">seq</font></span>)</span></span>)</span> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">seq'</font></span>)</span>

; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
