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<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">CQC-WFF</a> ;<br/><b>let </b><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font>, <font color="Maroon" title="c4">r</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">CQC-WFF</a> ;<br/>







<a NAME="E1:12"/>
for <font color="Olive" title="b1">T</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">CQC-WFF</a>   st <font color="Olive" title="b1">T</font> <a href="cqc_the1.html#NR1" title="CQC_THE1:NR.1">is_a_theory</a>  &amp; <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">T</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">=&gt;</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">'&amp;'</a> <font color="Maroon" title="c4">r</font></span>)</span></span>)</span> <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">=&gt;</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">'&amp;'</a> <font color="Maroon" title="c4">r</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">T</font>
 
<b>by </b><i><a class="ref" href="cqc_the1.html#D1" target="_self" title="CQC_THE1:def.1">Def1</a></i>;<br/>
<b>hence </b><a NAME="E2:12"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">=&gt;</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">'&amp;'</a> <font color="Maroon" title="c4">r</font></span>)</span></span>)</span> <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">=&gt;</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">'&amp;'</a> <font color="Maroon" title="c4">r</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_the1.html#K1" title="CQC_THE1:func.1">Cn</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="cqc_the1.html#D2" target="_self" title="CQC_THE1:def.2">Def2</a></i>;<br/>


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