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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">p</font>, <font color="Olive" title="b2">q</font> being    <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> <font color="Maroon" title="c1">A</font><br/>  for <font color="Olive" title="b3">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="b4">x</font>, <font color="Olive" title="b5">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>  st <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">h</font> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Olive" title="b4">x</font> &amp; <font color="Olive" title="b2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">h</font> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Olive" title="b5">y</font> &amp;  not <font color="Olive" title="b5">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="b3">h</font> holds <br/><font color="Olive" title="b1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">Ex</a> (<font color="Olive" title="b5">y</font>,<font color="Olive" title="b2">q</font>)</span>)</span> is  <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">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> <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">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="b2">x</font>, <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>  st <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">h</font> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Olive" title="b2">x</font> &amp; <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">h</font> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Olive" title="b3">y</font> &amp;  not <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">h</font> holds <br/><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">Ex</a> (<font color="Olive" title="b3">y</font>,<font color="Maroon" title="c3">q</font>)</span>)</span> is  <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c4">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">x</font>, <font color="Olive" title="b2">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>  st <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h</font> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h</font> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Olive" title="b2">y</font> &amp;  not <font color="Olive" title="b2">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="c4">h</font> holds <br/><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">Ex</a> (<font color="Olive" title="b2">y</font>,<font color="Maroon" title="c3">q</font>)</span>)</span> is  <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c5">x</font>, <font color="Maroon" title="c6">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="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h</font> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Maroon" title="c5">x</font> &amp; <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h</font> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Maroon" title="c6">y</font> &amp;  not <font color="Maroon" title="c6">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="c4">h</font> implies <font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">Ex</a> (<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c3">q</font>)</span>)</span> is  <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a>  )</span><br/>











<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:28"/><span class="lab"><font color="Green" title="E32">A1</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h</font> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Maroon" title="c5">x</font>
 <span class="kw">and </span><br/><a NAME="E2:28"/><span class="lab"><font color="Green" title="E33">A2</font></span>: 
<font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h</font> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Maroon" title="c6">y</font>
 <span class="kw">and </span><br/><a NAME="E3:28"/><span class="lab"><font color="Green" title="E34">A3</font></span>: 
 not <font color="Maroon" title="c6">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="c4">h</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="c2">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">Ex</a> (<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c3">q</font>)</span>)</span> is  <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a> </span><br/>

<span class="lab"><font color="Green" title="E35">A4</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">Ex</a> (<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c3">q</font>)</span>)</span></span>)</span> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Maroon" title="c5">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">Ex</a> (<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c3">q</font>)</span>)</span> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Maroon" title="c5">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the2.html#T12" target="_self" onmouseover="rs('cqc_the2/T12')" onmouseout="rh()">Th12</a></span>
<br/>.= 
<font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">Ex</a> (<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c3">q</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="ref" href="cqc_lang.html#T27" onmouseover="rs('cqc_lang/T27')" onmouseout="rh()">CQC_LANG:27</a></span>
;<br/>
<a NAME="E5:28"/>
 not <font color="Maroon" title="c6">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"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">Ex</a> (<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c3">q</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the2.html#T6" target="_self" onmouseover="rs('cqc_the2/T6')" onmouseout="rh()">Th6</a></span>;<br/>
<a NAME="E6:28"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A5</font></span>: 
 not <font color="Maroon" title="c6">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="c4">h</font> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">Ex</a> (<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c3">q</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:28"><span class="lab"><font color="Green" title="E34">A3</font></span></a>, <a class="ref" href="cqc_the2.html#T7" target="_self" onmouseover="rs('cqc_the2/T7')" onmouseout="rh()">Th7</a></span>;<br/>
<a NAME="E7:28"/><span class="lab"><font color="Green" title="E37">A6</font></span>: 
<font color="Maroon" title="c3">q</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">Ex</a> (<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c3">q</font>)</span>)</span> is  <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the2.html#T15" target="_self" onmouseover="rs('cqc_the2/T15')" onmouseout="rh()">Th15</a></span>;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">Ex</a> (<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c3">q</font>)</span>)</span></span>)</span> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Maroon" title="c6">y</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Maroon" title="c6">y</font></span>)</span> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">Ex</a> (<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c3">q</font>)</span>)</span> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Maroon" title="c6">y</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the2.html#T12" target="_self" onmouseover="rs('cqc_the2/T12')" onmouseout="rh()">Th12</a></span>
<br/>.= 
<font color="Maroon" title="c3">q</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">Ex</a> (<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c3">q</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:28"><span class="lab"><font color="Green" title="E33">A2</font></span></a>, <a class="ref" href="cqc_lang.html#T27" onmouseover="rs('cqc_lang/T27')" onmouseout="rh()">CQC_LANG:27</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E9:28"/>
<font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">Ex</a> (<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c3">q</font>)</span>)</span> is  <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:28"><span class="lab"><font color="Green" title="E37">A6</font></span></a>, <a class="txt" href="#E4:28"><span class="lab"><font color="Green" title="E35">A4</font></span></a>, <a class="txt" href="#E6:28"><span class="lab"><font color="Green" title="E36">A5</font></span></a>, <a class="ref" href="cqc_the1.html#T68" onmouseover="rs('cqc_the1/T68')" onmouseout="rh()">CQC_THE1:68</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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