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

<span class="kw">let </span><font color="Maroon" title="c1">p1</font>, <font color="Maroon" title="c2">p2</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( not <font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font> <a href="xboole_0.html#R3" title="XBOOLE_0:pred.3">are_c=-comparable</a>  implies <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> is  <a href="trees_1.html#V2" title="TREES_1:attr.2">AntiChain_of_Prefixes-like</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:90"/><span class="lab"><font color="Green" title="E37">A1</font></span>: 
not <font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font> <a href="xboole_0.html#R3" title="XBOOLE_0:pred.3">are_c=-comparable</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> is  <a href="trees_1.html#V2" title="TREES_1:attr.2">AntiChain_of_Prefixes-like</a> </span><br/>

<span class="kw">thus </span><a NAME="E2:90"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> holds <br/><font color="Olive" title="b1">x</font> is   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="trees_1.html#D13" target="_self" title="TREES_1:def.13">TREES_1:def 13</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">p1</font>, <font color="Olive" title="b2">p2</font> being  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  st <font color="Olive" title="b1">p1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <font color="Olive" title="b2">p2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <font color="Olive" title="b1">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">p2</font> holds <br/> not <font color="Olive" title="b1">p1</font>,<font color="Olive" title="b2">p2</font> <a href="xboole_0.html#R3" title="XBOOLE_0:pred.3">are_c=-comparable</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">q1</font>, <font color="Maroon" title="c4">q2</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</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="c3">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <font color="Maroon" title="c4">q2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <font color="Maroon" title="c3">q1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">q2</font> implies  not <font color="Maroon" title="c3">q1</font>,<font color="Maroon" title="c4">q2</font> <a href="xboole_0.html#R3" title="XBOOLE_0:pred.3">are_c=-comparable</a>  )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E3:90"/><span class="lab"><font color="Green" title="E38">A2</font></span>: 
<font color="Maroon" title="c3">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <span class="kw">and </span><br/><a NAME="E4:90"/><span class="lab"><font color="Green" title="E39">A3</font></span>: 
<font color="Maroon" title="c4">q2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c3">q1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">q2</font> or  not <font color="Maroon" title="c3">q1</font>,<font color="Maroon" title="c4">q2</font> <a href="xboole_0.html#R3" title="XBOOLE_0:pred.3">are_c=-comparable</a>  )</span><br/>

<a NAME="E5:90"/><span class="lab"><font color="Green" title="E40">A4</font></span>: 
( <font color="Maroon" title="c3">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p1</font> or <font color="Maroon" title="c3">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:90"><span class="lab"><font color="Green" title="E38">A2</font></span></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/>
<a NAME="E6:90"/><span class="lab"><font color="Green" title="E41">A5</font></span>: 
( <font color="Maroon" title="c4">q2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p1</font> or <font color="Maroon" title="c4">q2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:90"><span class="lab"><font color="Green" title="E39">A3</font></span></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/>
<span class="kw">thus </span><a NAME="E7:90"/>
(  not <font color="Maroon" title="c3">q1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">q2</font> or  not <font color="Maroon" title="c3">q1</font>,<font color="Maroon" title="c4">q2</font> <a href="xboole_0.html#R3" title="XBOOLE_0:pred.3">are_c=-comparable</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:90"><span class="lab"><font color="Green" title="E37">A1</font></span></a>, <a class="txt" href="#E5:90"><span class="lab"><font color="Green" title="E40">A4</font></span></a>, <a class="txt" href="#E6:90"><span class="lab"><font color="Green" title="E41">A5</font></span></a></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>
