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<span class="kw">let </span><font color="Maroon" title="c1">B</font>, <font color="Maroon" title="c2">C</font> be   <a href="polnot_1.html#NM2" title="POLNOT_1:NM.2">antichain</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"> <font color="Maroon" title="c1">B</font> <a href="polnot_1.html#K2" title="POLNOT_1:func.2">^</a> <font color="Maroon" title="c2">C</font> is  <a href="polnot_1.html#V3" title="POLNOT_1:attr.3">antichain-like</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">p</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="polnot_1.html#D16" target="_self" onmouseover="rs('polnot_1/D16')" onmouseout="rh()">POLNOT_1:def 16</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">  for <font color="Olive" title="b1">q</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  st <font color="Maroon" title="c3">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">B</font> <a href="polnot_1.html#K2" title="POLNOT_1:func.2">^</a> <font color="Maroon" title="c2">C</font> &amp; <font color="Maroon" title="c3">p</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b1">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">B</font> <a href="polnot_1.html#K2" title="POLNOT_1:func.2">^</a> <font color="Maroon" title="c2">C</font> holds <br/><font color="Olive" title="b1">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c4">q</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</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"> ( <font color="Maroon" title="c3">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">B</font> <a href="polnot_1.html#K2" title="POLNOT_1:func.2">^</a> <font color="Maroon" title="c2">C</font> &amp; <font color="Maroon" title="c3">p</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c4">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">B</font> <a href="polnot_1.html#K2" title="POLNOT_1:func.2">^</a> <font color="Maroon" title="c2">C</font> implies <font color="Maroon" title="c4">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:74"/><span class="lab"><font color="Green" title="E48">A3</font></span>: 
<font color="Maroon" title="c3">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">B</font> <a href="polnot_1.html#K2" title="POLNOT_1:func.2">^</a> <font color="Maroon" title="c2">C</font>
 <span class="kw">and </span><br/><a NAME="E2:74"/><span class="lab"><font color="Green" title="E49">A4</font></span>: 
<font color="Maroon" title="c3">p</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c4">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">B</font> <a href="polnot_1.html#K2" title="POLNOT_1:func.2">^</a> <font color="Maroon" title="c2">C</font>
 ; <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">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/>

<span class="kw">consider </span><font color="Maroon" title="c5">r</font>, <font color="Maroon" title="c6">s</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><span class="kw"> such that </span><br/><a NAME="E4:74"/><span class="lab"><font color="Green" title="E50">A7</font></span>: 
<font color="Maroon" title="c3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">r</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c6">s</font>
 <span class="kw">and </span><br/><a NAME="E5:74"/><span class="lab"><font color="Green" title="E51">A8</font></span>: 
<font color="Maroon" title="c5">r</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">B</font>
 <span class="kw">and </span><br/><a NAME="E6:74"/><span class="lab"><font color="Green" title="E52">A9</font></span>: 
<font color="Maroon" title="c6">s</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:74"><span class="lab"><font color="Green" title="E48">A3</font></span></a>, <a class="ref" href="polnot_1.html#D2" target="_self" onmouseover="rs('polnot_1/D2')" onmouseout="rh()">Def2</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c7">t</font>, <font color="Maroon" title="c8">u</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><span class="kw"> such that </span><br/><a NAME="E8:74"/><span class="lab"><font color="Green" title="E53">A10</font></span>: 
<font color="Maroon" title="c3">p</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c4">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">t</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c8">u</font>
 <span class="kw">and </span><br/><a NAME="E9:74"/><span class="lab"><font color="Green" title="E54">A11</font></span>: 
<font color="Maroon" title="c7">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">B</font>
 <span class="kw">and </span><br/><a NAME="E10:74"/><span class="lab"><font color="Green" title="E55">A12</font></span>: 
<font color="Maroon" title="c8">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:74"><span class="lab"><font color="Green" title="E49">A4</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="E11:74"/>
<font color="Maroon" title="c7">t</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c8">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">r</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c4">q</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:74"><span class="lab"><font color="Green" title="E50">A7</font></span></a>, <a class="txt" href="#E8:74"><span class="lab"><font color="Green" title="E53">A10</font></span></a>, <a class="ref" href="finseq_1.html#T32" onmouseover="rs('finseq_1/T32')" onmouseout="rh()">FINSEQ_1:32</a></span>;<br/>
<a NAME="E12:74"/><span class="kw">then </span>
<font color="Maroon" title="c8">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c4">q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:74"><span class="lab"><font color="Green" title="E51">A8</font></span></a>, <a class="txt" href="#E9:74"><span class="lab"><font color="Green" title="E54">A11</font></span></a>, <a class="ref" href="polnot_1.html#T43" target="_self" onmouseover="rs('polnot_1/T43')" onmouseout="rh()">Th43</a></span>;<br/>
<span class="kw">hence </span><a NAME="E13:74"/>
<font color="Maroon" title="c4">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:74"><span class="lab"><font color="Green" title="E52">A9</font></span></a>, <a class="txt" href="#E10:74"><span class="lab"><font color="Green" title="E55">A12</font></span></a>, <a class="ref" href="polnot_1.html#D16" target="_self" onmouseover="rs('polnot_1/D16')" onmouseout="rh()">Def16</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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