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<span class="kw">consider </span><font color="Maroon" title="c2">d1</font>, <font color="Maroon" title="c3">d2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D</font><span class="kw"> such that </span><br/><a NAME="E2:209_1_1"/><span class="lab"><font color="Green" title="E143">A1</font></span>: 
<font color="Maroon" title="c2">d1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">d2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="subset_1.html#D7" onmouseover="rs('subset_1/D7')" onmouseout="rh()">SUBSET_1:def 7</a></span>;<br/>
<span class="kw">take </span><font color="Maroon" title="c4">f</font> = <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c2">d1</font>,<font color="Maroon" title="c3">d2</font>,<font color="Maroon" title="c2">d1</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">f</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">V25</a>() &amp; <font color="Maroon" title="c4">f</font> is  <a href="finseq_6.html#V1" title="FINSEQ_6:attr.1">circular</a>  )</span><br/>

<a NAME="E3:209_1_1"/><span class="lab"><font color="Green" title="E144">A2</font></span>: 
( <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">d1</font> &amp; <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">d2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T45" onmouseover="rs('finseq_1/T45')" onmouseout="rh()">FINSEQ_1:45</a></span>;<br/>
<a NAME="E4:209_1_1"/>
( 1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c4">f</font> &amp; 2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c4">f</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T81" onmouseover="rs('finseq_1/T81')" onmouseout="rh()">FINSEQ_1:81</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:209_1_1"/>
<font color="Maroon" title="c4">f</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">V25</a>()
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:209_1_1"><span class="lab"><font color="Green" title="E143">A1</font></span></a>, <a class="txt" href="#E3:209_1_1"><span class="lab"><font color="Green" title="E144">A2</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">f</font> is  <a href="finseq_6.html#V1" title="FINSEQ_6:attr.1">circular</a> </span><br/>

<a NAME="E6:209_1_1"/><span class="lab"><font color="Green" title="E145">A3</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T45" onmouseover="rs('finseq_1/T45')" onmouseout="rh()">FINSEQ_1:45</a></span>;<br/>
<span class="kw">thus </span><font color="Maroon" title="c4">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1 = 
<font color="Maroon" title="c2">d1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_4.html#T18" onmouseover="rs('finseq_4/T18')" onmouseout="rh()">FINSEQ_4:18</a></span>
<br/>.= 
<font color="Maroon" title="c4">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">f</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:209_1_1"><span class="lab"><font color="Green" title="E145">A3</font></span></a>, <a class="ref" href="finseq_4.html#T18" onmouseover="rs('finseq_4/T18')" onmouseout="rh()">FINSEQ_4:18</a></span>
; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="finseq_6.html#D1" target="_self" onmouseover="rs('finseq_6/D1')" onmouseout="rh()">FINSEQ_6:def 1</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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