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

<b>let </b><font color="Maroon">F</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> ;<br/><b>let </b><font color="Maroon">G</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> ;<br/>



<b>thus </b> <a href="qc_lang2.html#K15" target="_self">Subformulae</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="qc_lang2.html#K3" target="_self">'or'</a> <font color="Maroon">G</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="qc_lang2.html#K15" target="_self">Subformulae</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">F</font></span>)</span> <a href="qc_lang1.html#K13">'&amp;'</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">G</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="qc_lang2.html#K3" target="_self">'or'</a> <font color="Maroon">G</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qc_lang2.html#K15" target="_self">Subformulae</a> <span class="p4">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">F</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="qc_lang2.html#K15" target="_self">Subformulae</a> <span class="p4">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">G</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">F</font></span>)</span> <a href="qc_lang1.html#K13">'&amp;'</a> <span class="p4">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">G</font></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="qc_lang2.html#K3" target="_self">'or'</a> <font color="Maroon">G</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="qc_lang2.html#T45" target="_self">Th45</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qc_lang2.html#K15" target="_self">Subformulae</a> <span class="p4">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">F</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="qc_lang2.html#K15" target="_self">Subformulae</a> <font color="Maroon">G</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">G</font></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">F</font></span>)</span> <a href="qc_lang1.html#K13">'&amp;'</a> <span class="p4">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">G</font></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="qc_lang2.html#K3" target="_self">'or'</a> <font color="Maroon">G</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="qc_lang2.html#K15" target="_self">Subformulae</a> <font color="Maroon">F</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">F</font></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="qc_lang2.html#K15" target="_self">Subformulae</a> <font color="Maroon">G</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">G</font></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">F</font></span>)</span> <a href="qc_lang1.html#K13">'&amp;'</a> <span class="p4">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">G</font></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="qc_lang2.html#K3" target="_self">'or'</a> <font color="Maroon">G</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qc_lang2.html#K15" target="_self">Subformulae</a> <font color="Maroon">F</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="qc_lang2.html#K15" target="_self">Subformulae</a> <font color="Maroon">G</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">G</font></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">F</font></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">F</font></span>)</span> <a href="qc_lang1.html#K13">'&amp;'</a> <span class="p4">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">G</font></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="qc_lang2.html#K3" target="_self">'or'</a> <font color="Maroon">G</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qc_lang2.html#K15" target="_self">Subformulae</a> <font color="Maroon">F</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="qc_lang2.html#K15" target="_self">Subformulae</a> <font color="Maroon">G</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">G</font></span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">F</font></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">F</font></span>)</span> <a href="qc_lang1.html#K13">'&amp;'</a> <span class="p4">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">G</font></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="qc_lang2.html#K3" target="_self">'or'</a> <font color="Maroon">G</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qc_lang2.html#K15" target="_self">Subformulae</a> <font color="Maroon">F</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="qc_lang2.html#K15" target="_self">Subformulae</a> <font color="Maroon">G</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K2">{</a><span class="default"><span class="p5">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">G</font></span>)</span>,<span class="p5">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">F</font></span>)</span></span><a href="tarski.html#K2">}</a></span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">F</font></span>)</span> <a href="qc_lang1.html#K13">'&amp;'</a> <span class="p4">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">G</font></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="qc_lang2.html#K3" target="_self">'or'</a> <font color="Maroon">G</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T41">ENUMSET1:41</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="qc_lang2.html#K15" target="_self">Subformulae</a> <font color="Maroon">F</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="qc_lang2.html#K15" target="_self">Subformulae</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K2">{</a><span class="default"><span class="p4">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">G</font></span>)</span>,<span class="p4">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">F</font></span>)</span></span><a href="tarski.html#K2">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">F</font></span>)</span> <a href="qc_lang1.html#K13">'&amp;'</a> <span class="p4">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">G</font></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="qc_lang2.html#K3" target="_self">'or'</a> <font color="Maroon">G</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qc_lang2.html#K15" target="_self">Subformulae</a> <font color="Maroon">F</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="qc_lang2.html#K15" target="_self">Subformulae</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K2">{</a><span class="default"><span class="p3">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">G</font></span>)</span>,<span class="p3">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">F</font></span>)</span></span><a href="tarski.html#K2">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">F</font></span>)</span> <a href="qc_lang1.html#K13">'&amp;'</a> <span class="p4">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">G</font></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="qc_lang2.html#K3" target="_self">'or'</a> <font color="Maroon">G</font></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qc_lang2.html#K15" target="_self">Subformulae</a> <font color="Maroon">F</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="qc_lang2.html#K15" target="_self">Subformulae</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K2">{</a><span class="default"><span class="p3">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">G</font></span>)</span>,<span class="p3">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">F</font></span>)</span></span><a href="tarski.html#K2">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">F</font></span>)</span> <a href="qc_lang1.html#K13">'&amp;'</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">G</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="qc_lang2.html#K3" target="_self">'or'</a> <font color="Maroon">G</font></span>)</span></span><a href="tarski.html#K2">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T41">ENUMSET1:41</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang2.html#K15" target="_self">Subformulae</a> <font color="Maroon">F</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="qc_lang2.html#K15" target="_self">Subformulae</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K2">{</a><span class="default"><span class="p3">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">G</font></span>)</span>,<span class="p3">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">F</font></span>)</span></span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K2">{</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">F</font></span>)</span> <a href="qc_lang1.html#K13">'&amp;'</a> <span class="p4">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">G</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="qc_lang2.html#K3" target="_self">'or'</a> <font color="Maroon">G</font></span>)</span></span><a href="tarski.html#K2">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang2.html#K15" target="_self">Subformulae</a> <font color="Maroon">F</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="qc_lang2.html#K15" target="_self">Subformulae</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">G</font></span>)</span>,<span class="p2">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">F</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">F</font></span>)</span> <a href="qc_lang1.html#K13">'&amp;'</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">G</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="qc_lang2.html#K3" target="_self">'or'</a> <font color="Maroon">G</font></span>)</span></span><a href="enumset1.html#K2">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T45">ENUMSET1:45</a></i>
;<br/>


</div>
