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<span class="kw">let </span><font color="Maroon" title="c1">T</font> be   <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</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">t</font> being   <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of <font color="Maroon" title="c1">T</font> holds  <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b1">t</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is    <a href="trees_1.html#M4" title="TREES_1:mode.4">AntiChain_of_Prefixes</a> of <font color="Maroon" title="c1">T</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">t</font> be    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of <font color="Maroon" title="c1">T</font>; <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#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">t</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is    <a href="trees_1.html#M4" title="TREES_1:mode.4">AntiChain_of_Prefixes</a> of <font color="Maroon" title="c1">T</font></span><br/>



<span class="kw">reconsider </span><font color="Maroon" title="c3">S</font> = <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">t</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> as   <a href="trees_1.html#NM5" title="TREES_1:NM.5">AntiChain_of_Prefixes</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="trees_1.html#T70" target="_self" title="TREES_1:th.70">Th70</a></span>;<br/>
<a NAME="E2:94"/><span class="lab"><font color="Green" title="E39">A1</font></span>: 
<font color="Maroon" title="c3">S</font> is    <a href="trees_1.html#M4" title="TREES_1:mode.4">AntiChain_of_Prefixes</a> of <font color="Maroon" title="c1">T</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="94_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a>,<a class="ref" href="trees_1.html#D14" target="_self" title="TREES_1:def.14">TREES_1:def 14</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="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">S</font> or <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">T</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:94_1"/><span class="lab"><font color="Green" title="E40">A2</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">S</font>
 ; <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="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">T</font></span><br/>

<a NAME="E2:94_1"/><span class="lab"><font color="Green" title="E41">A3</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">t</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:94_1"><span class="lab"><font color="Green" title="E40">A2</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<span class="kw">thus </span><a NAME="E3:94_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:94_1"><span class="lab"><font color="Green" title="E41">A3</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><span class="kw">end;</span></div>
<span class="kw">thus </span><a NAME="E3:94"/>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">t</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is    <a href="trees_1.html#M4" title="TREES_1:mode.4">AntiChain_of_Prefixes</a> of <font color="Maroon" title="c1">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:94"><span class="lab"><font color="Green" title="E39">A1</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/>


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