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<span class="kw">let </span><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">q</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="substut1.html#K9" title="SUBSTUT1:func.9">Bound_Vars</a> <font color="Maroon" title="c1">p</font> &amp;  <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c2">q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="substut1.html#K9" title="SUBSTUT1:func.9">Bound_Vars</a> <font color="Maroon" title="c2">q</font> implies  <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="substut1.html#K9" title="SUBSTUT1:func.9">Bound_Vars</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span> )</span><br/>



<a NAME="E1:60"/><span class="lab"><font color="Green" title="E45">A1</font></span>: 
 <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c2">q</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang3.html#T10" title="QC_LANG3:th.10">QC_LANG3:10</a></span>;<br/>
<a NAME="E2:60"/>
<font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c2">q</font> is  <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#D18" title="QC_LANG1:def.18">QC_LANG1:def 18</a></span>;<br/>
<a NAME="E3:60"/><span class="kw">then </span>
 <a href="substut1.html#K9" title="SUBSTUT1:func.9">Bound_Vars</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="substut1.html#K9" title="SUBSTUT1:func.9">Bound_Vars</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K18" title="QC_LANG1:func.18">the_left_argument_of</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="substut1.html#K9" title="SUBSTUT1:func.9">Bound_Vars</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K19" title="QC_LANG1:func.19">the_right_argument_of</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="substut1.html#T5" title="SUBSTUT1:th.5">SUBSTUT1:5</a></span>;<br/>
<a NAME="E4:60"/><span class="kw">then </span>
 <a href="substut1.html#K9" title="SUBSTUT1:func.9">Bound_Vars</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="substut1.html#K9" title="SUBSTUT1:func.9">Bound_Vars</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="substut1.html#K9" title="SUBSTUT1:func.9">Bound_Vars</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K19" title="QC_LANG1:func.19">the_right_argument_of</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang2.html#T4" title="QC_LANG2:th.4">QC_LANG2:4</a></span>;<br/>
<a NAME="E5:60"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A2</font></span>: 
 <a href="substut1.html#K9" title="SUBSTUT1:func.9">Bound_Vars</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="substut1.html#K9" title="SUBSTUT1:func.9">Bound_Vars</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="substut1.html#K9" title="SUBSTUT1:func.9">Bound_Vars</a> <font color="Maroon" title="c2">q</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang2.html#T4" title="QC_LANG2:th.4">QC_LANG2:4</a></span>;<br/>
<span class="kw">assume </span><a NAME="E6:60"/>
(  <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="substut1.html#K9" title="SUBSTUT1:func.9">Bound_Vars</a> <font color="Maroon" title="c1">p</font> &amp;  <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c2">q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="substut1.html#K9" title="SUBSTUT1:func.9">Bound_Vars</a> <font color="Maroon" title="c2">q</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="substut1.html#K9" title="SUBSTUT1:func.9">Bound_Vars</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span></span><br/>

<span class="kw">hence </span><a NAME="E7:60"/>
 <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="substut1.html#K9" title="SUBSTUT1:func.9">Bound_Vars</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:60"><span class="lab"><font color="Green" title="E46">A2</font></span></a>, <a class="txt" href="#E1:60"><span class="lab"><font color="Green" title="E45">A1</font></span></a>, <a class="ref" href="xboole_1.html#T13" title="XBOOLE_1:th.13">XBOOLE_1:13</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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