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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#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">A</font> being non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/> for <font color="Olive" title="b2">J</font> being   <a href="valuat_1.html#M1" title="VALUAT_1:mode.1">interpretation</a> of <font color="Olive" title="b1">A</font>  st ( for <font color="Olive" title="b3">v</font>, <font color="Olive" title="b4">w</font> being   <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Olive" title="b1">A</font>  st <font color="Olive" title="b3">v</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</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="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b4">w</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</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> holds <br/>( <font color="Olive" title="b2">J</font>,<font color="Olive" title="b3">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c1">p</font> iff <font color="Olive" title="b2">J</font>,<font color="Olive" title="b4">w</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c1">p</font> ) ) &amp; ( for <font color="Olive" title="b3">v</font>, <font color="Olive" title="b4">w</font> being   <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Olive" title="b1">A</font>  st <font color="Olive" title="b3">v</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</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> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b4">w</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</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> holds <br/>( <font color="Olive" title="b2">J</font>,<font color="Olive" title="b3">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c2">q</font> iff <font color="Olive" title="b2">J</font>,<font color="Olive" title="b4">w</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c2">q</font> ) ) holds <br/>for <font color="Olive" title="b3">v</font>, <font color="Olive" title="b4">w</font> being   <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Olive" title="b1">A</font>  st <font color="Olive" title="b3">v</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b4">w</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span> holds <br/>( <font color="Olive" title="b2">J</font>,<font color="Olive" title="b3">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font> iff <font color="Olive" title="b2">J</font>,<font color="Olive" title="b4">w</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">A</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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">J</font> being   <a href="valuat_1.html#M1" title="VALUAT_1:mode.1">interpretation</a> of <font color="Maroon" title="c3">A</font>  st ( for <font color="Olive" title="b2">v</font>, <font color="Olive" title="b3">w</font> being   <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c3">A</font>  st <font color="Olive" title="b2">v</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</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="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b3">w</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</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> holds <br/>( <font color="Olive" title="b1">J</font>,<font color="Olive" title="b2">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c1">p</font> iff <font color="Olive" title="b1">J</font>,<font color="Olive" title="b3">w</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c1">p</font> ) ) &amp; ( for <font color="Olive" title="b2">v</font>, <font color="Olive" title="b3">w</font> being   <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c3">A</font>  st <font color="Olive" title="b2">v</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</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> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b3">w</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</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> holds <br/>( <font color="Olive" title="b1">J</font>,<font color="Olive" title="b2">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c2">q</font> iff <font color="Olive" title="b1">J</font>,<font color="Olive" title="b3">w</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c2">q</font> ) ) holds <br/>for <font color="Olive" title="b2">v</font>, <font color="Olive" title="b3">w</font> being   <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c3">A</font>  st <font color="Olive" title="b2">v</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b3">w</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span> holds <br/>( <font color="Olive" title="b1">J</font>,<font color="Olive" title="b2">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font> iff <font color="Olive" title="b1">J</font>,<font color="Olive" title="b3">w</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">J</font> be    <a href="valuat_1.html#M1" title="VALUAT_1:mode.1">interpretation</a> of <font color="Maroon" title="c3">A</font>; <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">v</font>, <font color="Olive" title="b2">w</font> being   <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c3">A</font>  st <font color="Olive" title="b1">v</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</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="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">w</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</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> holds <br/>( <font color="Maroon" title="c4">J</font>,<font color="Olive" title="b1">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c1">p</font> iff <font color="Maroon" title="c4">J</font>,<font color="Olive" title="b2">w</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c1">p</font> ) ) &amp; ( for <font color="Olive" title="b1">v</font>, <font color="Olive" title="b2">w</font> being   <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c3">A</font>  st <font color="Olive" title="b1">v</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</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> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">w</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</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> holds <br/>( <font color="Maroon" title="c4">J</font>,<font color="Olive" title="b1">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c2">q</font> iff <font color="Maroon" title="c4">J</font>,<font color="Olive" title="b2">w</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c2">q</font> ) ) implies for <font color="Olive" title="b1">v</font>, <font color="Olive" title="b2">w</font> being   <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c3">A</font>  st <font color="Olive" title="b1">v</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">w</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span> holds <br/>( <font color="Maroon" title="c4">J</font>,<font color="Olive" title="b1">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font> iff <font color="Maroon" title="c4">J</font>,<font color="Olive" title="b2">w</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font> ) )</span><br/>







<span class="kw">assume </span><a NAME="E1:82"/><span class="lab"><font color="Green" title="E62">A1</font></span>: 
( ( for <font color="Olive" title="b1">v</font>, <font color="Olive" title="b2">w</font> being   <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c3">A</font>  st <font color="Olive" title="b1">v</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</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="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">w</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</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> holds <br/>( <font color="Maroon" title="c4">J</font>,<font color="Olive" title="b1">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c1">p</font> iff <font color="Maroon" title="c4">J</font>,<font color="Olive" title="b2">w</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c1">p</font> ) ) &amp; ( for <font color="Olive" title="b1">v</font>, <font color="Olive" title="b2">w</font> being   <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c3">A</font>  st <font color="Olive" title="b1">v</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</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> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">w</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</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> holds <br/>( <font color="Maroon" title="c4">J</font>,<font color="Olive" title="b1">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c2">q</font> iff <font color="Maroon" title="c4">J</font>,<font color="Olive" title="b2">w</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c2">q</font> ) ) )
 ; <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">v</font>, <font color="Olive" title="b2">w</font> being   <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c3">A</font>  st <font color="Olive" title="b1">v</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">w</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span> holds <br/>( <font color="Maroon" title="c4">J</font>,<font color="Olive" title="b1">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font> iff <font color="Maroon" title="c4">J</font>,<font color="Olive" title="b2">w</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c5">X</font> = <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>;<br/>
<span class="kw">let </span><font color="Maroon" title="c6">v</font>, <font color="Maroon" title="c7">w</font> be    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c3">A</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="c6">v</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c7">w</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span> implies ( <font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c6">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font> iff <font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c7">w</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font> ) )</span><br/>



<a NAME="E2:82"/><span class="lab"><font color="Green" title="E63">A2</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#K8" title="CQC_LANG:func.8">'&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#T14" title="QC_LANG3:th.14">QC_LANG3:14</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:82"/>
<font color="Maroon" title="c6">v</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c7">w</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</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="c4">J</font>,<font color="Maroon" title="c6">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font> iff <font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c7">w</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font> )</span><br/>

<a NAME="E4:82"/><span class="kw">then </span>
( <font color="Maroon" title="c6">v</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</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="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c7">w</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</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> &amp; <font color="Maroon" title="c6">v</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</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> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c7">w</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</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="txt" href="#E2:82"><span class="lab"><font color="Green" title="E63">A2</font></span></a>, <a class="ref" href="relat_1.html#T188" title="RELAT_1:th.188">RELAT_1:188</a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></span>;<br/>
<a NAME="E5:82"/><span class="kw">then </span>
( <font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c6">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c1">p</font> &amp; <font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c6">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c2">q</font> iff ( <font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c7">w</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c1">p</font> &amp; <font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c7">w</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c2">q</font> ) )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:82"><span class="lab"><font color="Green" title="E62">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:82"/>
( <font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c6">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font> iff <font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c7">w</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="valuat_1.html#T29" title="VALUAT_1:th.29">VALUAT_1:29</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>
