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<span class="kw">let </span><font color="Maroon" title="c1">A</font> be    <a href="qc_lang1.html#M1" title="QC_LANG1:mode.1">QC-alphabet</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">s</font>, <font color="Olive" title="b2">h</font> being   <a href="qc_lang1.html#NM10" title="QC_LANG1:NM.10">QC-formula</a> of <font color="Maroon" title="c1">A</font><br/>  for <font color="Olive" title="b3">y</font> being   <a href="qc_lang1.html#NM5" title="QC_LANG1:NM.5">bound_QC-variable</a> of <font color="Maroon" title="c1">A</font> holds <br/> ( <font color="Olive" title="b3">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="qc_lang1.html#K24" title="QC_LANG1:func.24">still_not-bound_in</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">s</font> <a href="qc_lang1.html#K14" title="QC_LANG1:func.14">'&amp;'</a> <font color="Olive" title="b2">h</font></span>)</span> iff ( <font color="Olive" title="b3">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="qc_lang1.html#K24" title="QC_LANG1:func.24">still_not-bound_in</a> <font color="Olive" title="b1">s</font> or <font color="Olive" title="b3">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="qc_lang1.html#K24" title="QC_LANG1:func.24">still_not-bound_in</a> <font color="Olive" title="b2">h</font> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">s</font>, <font color="Maroon" title="c3">h</font> be   <a href="qc_lang1.html#NM10" title="QC_LANG1:NM.10">QC-formula</a> of <font color="Maroon" title="c1">A</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">y</font> being   <a href="qc_lang1.html#NM5" title="QC_LANG1:NM.5">bound_QC-variable</a> of <font color="Maroon" title="c1">A</font> holds <br/> ( <font color="Olive" title="b1">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="qc_lang1.html#K24" title="QC_LANG1:func.24">still_not-bound_in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="qc_lang1.html#K14" title="QC_LANG1:func.14">'&amp;'</a> <font color="Maroon" title="c3">h</font></span>)</span> iff ( <font color="Olive" title="b1">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="qc_lang1.html#K24" title="QC_LANG1:func.24">still_not-bound_in</a> <font color="Maroon" title="c2">s</font> or <font color="Olive" title="b1">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="qc_lang1.html#K24" title="QC_LANG1:func.24">still_not-bound_in</a> <font color="Maroon" title="c3">h</font> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">y</font> be   <a href="qc_lang1.html#NM5" title="QC_LANG1:NM.5">bound_QC-variable</a> of <font color="Maroon" title="c1">A</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="qc_lang1.html#K24" title="QC_LANG1:func.24">still_not-bound_in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="qc_lang1.html#K14" title="QC_LANG1:func.14">'&amp;'</a> <font color="Maroon" title="c3">h</font></span>)</span> iff ( <font color="Maroon" title="c4">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="qc_lang1.html#K24" title="QC_LANG1:func.24">still_not-bound_in</a> <font color="Maroon" title="c2">s</font> or <font color="Maroon" title="c4">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="qc_lang1.html#K24" title="QC_LANG1:func.24">still_not-bound_in</a> <font color="Maroon" title="c3">h</font> ) )</span><br/>







<a NAME="E1:14"/>
 <a href="qc_lang1.html#K24" title="QC_LANG1:func.24">still_not-bound_in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="qc_lang1.html#K14" title="QC_LANG1:func.14">'&amp;'</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K24" title="QC_LANG1:func.24">still_not-bound_in</a> <font color="Maroon" title="c2">s</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#K24" title="QC_LANG1:func.24">still_not-bound_in</a> <font color="Maroon" title="c3">h</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang3.html#T10" onmouseover="rs('qc_lang3/T10')" onmouseout="rh()">QC_LANG3:10</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:14"/>
( <font color="Maroon" title="c4">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="qc_lang1.html#K24" title="QC_LANG1:func.24">still_not-bound_in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="qc_lang1.html#K14" title="QC_LANG1:func.14">'&amp;'</a> <font color="Maroon" title="c3">h</font></span>)</span> iff ( <font color="Maroon" title="c4">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="qc_lang1.html#K24" title="QC_LANG1:func.24">still_not-bound_in</a> <font color="Maroon" title="c2">s</font> or <font color="Maroon" title="c4">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="qc_lang1.html#K24" title="QC_LANG1:func.24">still_not-bound_in</a> <font color="Maroon" title="c3">h</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D3" onmouseover="rs('xboole_0/D3')" onmouseout="rh()">XBOOLE_0:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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