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<span class="kw">let </span><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#K4" title="CQC_LANG:func.4">CQC-WFF</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">p</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> <br/> for <font color="Olive" title="b2">x</font> being  <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a>  st <font color="Maroon" title="c1">X</font> <a href="cqc_the1.html#R3" title="CQC_THE1:pred.3">|-</a> <font color="Olive" title="b1">p</font> holds <br/><font color="Maroon" title="c1">X</font> <a href="cqc_the1.html#R3" title="CQC_THE1:pred.3">|-</a>  <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Olive" title="b2">x</font>,<font color="Olive" title="b1">p</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">x</font> being  <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a>  st <font color="Maroon" title="c1">X</font> <a href="cqc_the1.html#R3" title="CQC_THE1:pred.3">|-</a> <font color="Maroon" title="c2">p</font> holds <br/><font color="Maroon" title="c1">X</font> <a href="cqc_the1.html#R3" title="CQC_THE1:pred.3">|-</a>  <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Olive" title="b1">x</font>,<font color="Maroon" title="c2">p</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">x</font> be   <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</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">X</font> <a href="cqc_the1.html#R3" title="CQC_THE1:pred.3">|-</a> <font color="Maroon" title="c2">p</font> implies <font color="Maroon" title="c1">X</font> <a href="cqc_the1.html#R3" title="CQC_THE1:pred.3">|-</a>  <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font> )</span><br/>





<a NAME="E1:110"/><span class="lab"><font color="Green" title="E72">A1</font></span>: 
<font color="Maroon" title="c1">X</font> <a href="cqc_the1.html#R3" title="CQC_THE1:pred.3">|-</a> <font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font></span>)</span></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c2">p</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the1.html#T98" title="CQC_THE1:th.98">CQC_THE1:98</a>, <a class="ref" href="lukasi_1.html#T45" title="LUKASI_1:th.45">LUKASI_1:45</a></span>;<br/>
<a NAME="E2:110"/>
not <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the2.html#T5" target="_self" title="CQC_THE2:th.5">Th5</a></span>;<br/>
<a NAME="E3:110"/><span class="kw">then </span><span class="lab"><font color="Green" title="E73">A2</font></span>: 
not <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the2.html#T7" target="_self" title="CQC_THE2:th.7">Th7</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:110"/>
<font color="Maroon" title="c1">X</font> <a href="cqc_the1.html#R3" title="CQC_THE1:pred.3">|-</a> <font color="Maroon" title="c2">p</font>
 ; <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">X</font> <a href="cqc_the1.html#R3" title="CQC_THE1:pred.3">|-</a>  <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font></span><br/>

<a NAME="E5:110"/><span class="kw">then </span>
<font color="Maroon" title="c1">X</font> <a href="cqc_the1.html#R3" title="CQC_THE1:pred.3">|-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font></span>)</span></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c2">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:110"><span class="lab"><font color="Green" title="E72">A1</font></span></a>, <a class="ref" href="cqc_the1.html#T92" title="CQC_THE1:th.92">CQC_THE1:92</a></span>;<br/>
<a NAME="E6:110"/><span class="kw">then </span><span class="lab"><font color="Green" title="E74">A3</font></span>: 
<font color="Maroon" title="c1">X</font> <a href="cqc_the1.html#R3" title="CQC_THE1:pred.3">|-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font></span>)</span></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:110"><span class="lab"><font color="Green" title="E73">A2</font></span></a>, <a class="ref" href="cqc_the1.html#T94" title="CQC_THE1:th.94">CQC_THE1:94</a></span>;<br/>
<a NAME="E7:110"/>
<font color="Maroon" title="c1">X</font> <a href="cqc_the1.html#R3" title="CQC_THE1:pred.3">|-</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the1.html#T98" title="CQC_THE1:th.98">CQC_THE1:98</a>, <a class="ref" href="lukasi_1.html#T44" title="LUKASI_1:th.44">LUKASI_1:44</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:110"/>
<font color="Maroon" title="c1">X</font> <a href="cqc_the1.html#R3" title="CQC_THE1:pred.3">|-</a>  <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:110"><span class="lab"><font color="Green" title="E74">A3</font></span></a>, <a class="ref" href="cqc_the1.html#T92" title="CQC_THE1:th.92">CQC_THE1:92</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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