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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">w</font> being   <a href="catalan2.html#M2" title="CATALAN2:mode.2">Element</a> of <font color="Maroon" title="c1">E</font> <a href="catalan2.html#K2" title="CATALAN2:func.2">^omega</a>  holds   <a href="rewrite2.html#K9" title="REWRITE2:func.9">Lang</a> <font color="Olive" title="b1">w</font>,<span class="p1">(<span class="default"><a href="rewrite2.html#K7" title="REWRITE2:func.7">id</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="catalan2.html#K2" title="CATALAN2:func.2">^omega</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="flang_1.html#K4" title="FLANG_1:func.4">{</a><span class="default"><font color="Olive" title="b1">w</font></span><a href="flang_1.html#K4" title="FLANG_1:func.4">}</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">w</font> be    <a href="catalan2.html#M2" title="CATALAN2:mode.2">Element</a> of <font color="Maroon" title="c1">E</font> <a href="catalan2.html#K2" title="CATALAN2:func.2">^omega</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="rewrite2.html#K9" title="REWRITE2:func.9">Lang</a> <font color="Maroon" title="c2">w</font>,<span class="p1">(<span class="default"><a href="rewrite2.html#K7" title="REWRITE2:func.7">id</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="catalan2.html#K2" title="CATALAN2:func.2">^omega</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="flang_1.html#K4" title="FLANG_1:func.4">{</a><span class="default"><font color="Maroon" title="c2">w</font></span><a href="flang_1.html#K4" title="FLANG_1:func.4">}</a></span></span><br/>



<span class="p1">(<span class="default"><a href="oposet_1.html#K1" title="OPOSET_1:func.1">{}</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="catalan2.html#K2" title="CATALAN2:func.2">^omega</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="catalan2.html#K2" title="CATALAN2:func.2">^omega</a> </span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="rewrite2.html#K7" title="REWRITE2:func.7">id</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="catalan2.html#K2" title="CATALAN2:func.2">^omega</a> </span>)</span></span>)</span> = 
<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="rewrite2.html#K7" title="REWRITE2:func.7">id</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="catalan2.html#K2" title="CATALAN2:func.2">^omega</a> </span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="oposet_1.html#D1" title="OPOSET_1:def.1">OPOSET_1:def 1</a></span>
<br/>.= 
 <a href="rewrite2.html#K7" title="REWRITE2:func.7">id</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="catalan2.html#K2" title="CATALAN2:func.2">^omega</a> </span>)</span>

;<br/>
<span class="kw">hence </span> <a href="rewrite2.html#K9" title="REWRITE2:func.9">Lang</a> <font color="Maroon" title="c2">w</font>,<span class="p1">(<span class="default"><a href="rewrite2.html#K7" title="REWRITE2:func.7">id</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="catalan2.html#K2" title="CATALAN2:func.2">^omega</a> </span>)</span></span>)</span> = 
 <a href="rewrite2.html#K9" title="REWRITE2:func.9">Lang</a> <font color="Maroon" title="c2">w</font>,<span class="p1">(<span class="default"><a href="oposet_1.html#K1" title="OPOSET_1:func.1">{}</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="catalan2.html#K2" title="CATALAN2:func.2">^omega</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="catalan2.html#K2" title="CATALAN2:func.2">^omega</a> </span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite2.html#T49" target="_self" title="REWRITE2:th.49">Th49</a></span>
<br/>.= 
<span class="p1"><a href="flang_1.html#K4" title="FLANG_1:func.4">{</a><span class="default"><font color="Maroon" title="c2">w</font></span><a href="flang_1.html#K4" title="FLANG_1:func.4">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite2.html#T50" target="_self" title="REWRITE2:th.50">Th50</a></span>
;<br/> <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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