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<b>let </b><font color="Maroon" title="c1">E</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">B</font>, <font color="Olive" title="b2">A</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="catalan2.html#K3" title="CATALAN2:func.3">^omega</a> </span>)</span><br/> for <font color="Olive" title="b3">l</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st  <a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c1">E</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">B</font> holds <br/>( <font color="Olive" title="b2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">A</font> <a href="flang_1.html#K6" title="FLANG_1:func.6">^^</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">B</font> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Olive" title="b3">l</font></span>)</span> &amp; <font color="Olive" title="b2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">B</font> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Olive" title="b3">l</font></span>)</span> <a href="flang_1.html#K6" title="FLANG_1:func.6">^^</a> <font color="Olive" title="b2">A</font> )</span><br/><b>let </b><font color="Maroon" title="c2">B</font>, <font color="Maroon" title="c3">A</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="catalan2.html#K3" title="CATALAN2:func.3">^omega</a> </span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">l</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st  <a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c1">E</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B</font> holds <br/>( <font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">A</font> <a href="flang_1.html#K6" title="FLANG_1:func.6">^^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Olive" title="b1">l</font></span>)</span> &amp; <font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Olive" title="b1">l</font></span>)</span> <a href="flang_1.html#K6" title="FLANG_1:func.6">^^</a> <font color="Maroon" title="c3">A</font> )</span><br/><b>let </b><font color="Maroon" title="c4">l</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c1">E</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B</font> implies ( <font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">A</font> <a href="flang_1.html#K6" title="FLANG_1:func.6">^^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Maroon" title="c4">l</font></span>)</span> &amp; <font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Maroon" title="c4">l</font></span>)</span> <a href="flang_1.html#K6" title="FLANG_1:func.6">^^</a> <font color="Maroon" title="c3">A</font> ) )</span><br/>







<b>assume </b><a NAME="E1:13"/>
 <a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c1">E</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">A</font> <a href="flang_1.html#K6" title="FLANG_1:func.6">^^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Maroon" title="c4">l</font></span>)</span> &amp; <font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Maroon" title="c4">l</font></span>)</span> <a href="flang_1.html#K6" title="FLANG_1:func.6">^^</a> <font color="Maroon" title="c3">A</font> )</span><br/>

<a NAME="E2:13"/><b>then </b>
 <a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c1">E</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B</font> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Maroon" title="c4">l</font>
 
<b>by </b><i><a class="ref" href="flang_1.html#T31" title="FLANG_1:th.31">FLANG_1:31</a></i>;<br/>
<b>hence </b><a NAME="E3:13"/>
( <font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">A</font> <a href="flang_1.html#K6" title="FLANG_1:func.6">^^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Maroon" title="c4">l</font></span>)</span> &amp; <font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Maroon" title="c4">l</font></span>)</span> <a href="flang_1.html#K6" title="FLANG_1:func.6">^^</a> <font color="Maroon" title="c3">A</font> )
 <b>by </b><i><a class="ref" href="flang_1.html#T17" title="FLANG_1:th.17">FLANG_1:17</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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