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<span class="kw">set </span><font color="Maroon" title="c3">p</font> =  the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E2:6_1_1"/><span class="lab"><font color="Green" title="E2">A1</font></span>: 
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">T</font>
 <span class="kw">and </span><br/><a NAME="E3:6_1_1"/><span class="lab"><font color="Green" title="E3">A2</font></span>: 
<font color="Maroon" title="c5">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">T</font>
 <span class="kw">and </span><br/><a NAME="E4:6_1_1"/><span class="lab"><font color="Green" title="E4">A3</font></span>: 
<font color="Maroon" title="c4">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#D10" onmouseover="rs('zfmisc_1/D10')" onmouseout="rh()">ZFMISC_1:def 10</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">q</font> = <font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c7">r</font> = <font color="Maroon" title="c5">b</font> as   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_1_1"><span class="lab"><font color="Green" title="E2">A1</font></span></a>, <a class="txt" href="#E3:6_1_1"><span class="lab"><font color="Green" title="E3">A2</font></span></a></span>;<br/>
<a NAME="E6:6_1_1"/><span class="lab"><font color="Green" title="E5">A5</font></span>: 
(  the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c6">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">S</font> <a href="polnot_1.html#K2" title="POLNOT_1:func.2">^</a> <font color="Maroon" title="c2">T</font> &amp;  the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c7">r</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">S</font> <a href="polnot_1.html#K2" title="POLNOT_1:func.2">^</a> <font color="Maroon" title="c2">T</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_1_1"><span class="lab"><font color="Green" title="E2">A1</font></span></a>, <a class="txt" href="#E3:6_1_1"><span class="lab"><font color="Green" title="E3">A2</font></span></a>, <a class="ref" href="polnot_1.html#D2" target="_self" onmouseover="rs('polnot_1/D2')" onmouseout="rh()">Def2</a></span>;<br/>
<a NAME="E7:6_1_1"/>
 the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c6">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c7">r</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:6_1_1"><span class="lab"><font color="Green" title="E4">A3</font></span></a>, <a class="ref" href="finseq_1.html#T33" onmouseover="rs('finseq_1/T33')" onmouseout="rh()">FINSEQ_1:33</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:6_1_1"/>
 not <font color="Maroon" title="c1">S</font> <a href="polnot_1.html#K2" title="POLNOT_1:func.2">^</a> <font color="Maroon" title="c2">T</font> is  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6_1_1"><span class="lab"><font color="Green" title="E5">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D10" onmouseover="rs('zfmisc_1/D10')" onmouseout="rh()">ZFMISC_1:def 10</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"> verum</span><br/>


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