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<span class="kw">thus </span><a NAME="E1:103"/>
 <a href="qc_lang2.html#K15" title="QC_LANG2:func.15">Subformulae</a> <a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
  <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a> <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"><a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="qc_lang2.html#K15" title="QC_LANG2:func.15">Subformulae</a> <a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a> </span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="103_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">a</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="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="qc_lang2.html#K15" title="QC_LANG2:func.15">Subformulae</a> <a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a>  or <font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:103_1"/>
<font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="qc_lang2.html#K15" title="QC_LANG2:func.15">Subformulae</a> <a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a> 
 ; <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="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c2">F</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a> <span class="kw"> such that </span><br/><a NAME="E3:103_1"/><span class="lab"><font color="Green" title="E52">A1</font></span>: 
<font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font>
 <span class="kw">and </span><br/><a NAME="E4:103_1"/><span class="lab"><font color="Green" title="E53">A2</font></span>: 
<font color="Maroon" title="c2">F</font> <a href="qc_lang2.html#R2" title="QC_LANG2:pred.2">is_subformula_of</a>  <a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang2.html#D23" target="_self" title="QC_LANG2:def.23">Def23</a></span>;<br/>
<a NAME="E5:103_1"/>
<font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:103_1"><span class="lab"><font color="Green" title="E53">A2</font></span></a>, <a class="ref" href="qc_lang2.html#T99" target="_self" title="QC_LANG2:th.99">Th99</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:103_1"/>
<font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:103_1"><span class="lab"><font color="Green" title="E52">A1</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</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">let </span><font color="Maroon" title="c1">a</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="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> or <font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="qc_lang2.html#K15" title="QC_LANG2:func.15">Subformulae</a> <a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E2:103"/>
<font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ; <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="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="qc_lang2.html#K15" title="QC_LANG2:func.15">Subformulae</a> <a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a> </span><br/>

<a NAME="E3:103"/><span class="kw">then </span>
<font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:103"/>
<font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="qc_lang2.html#K15" title="QC_LANG2:func.15">Subformulae</a> <a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang2.html#D23" target="_self" title="QC_LANG2:def.23">Def23</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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