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<span class="kw">let </span><font color="Maroon" title="c1">Al</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> 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">Al</font><br/>  for <font color="Olive" title="b2">Sub</font> being   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> of <font color="Maroon" title="c1">Al</font> holds   <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p2"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span></span>)</span></span><br/>

<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[   <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">Al</font>] <span class="kw">means </span> for <font color="Olive" title="b1">Sub</font> being   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> of <font color="Maroon" title="c1">Al</font> holds   <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p2"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default">$1,<font color="Olive" title="b1">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span></span>)</span>;<br/>
<a NAME="E1:36"/><span class="lab"><font color="Green" title="E21">A1</font></span>: 
 for <font color="Olive" title="b1">r</font>, <font color="Olive" title="b2">s</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">Al</font><br/>  for <font color="Olive" title="b3">x</font> being   <a href="qc_lang1.html#NM5" title="QC_LANG1:NM.5">bound_QC-variable</a> of <font color="Maroon" title="c1">Al</font><br/>  for <font color="Olive" title="b4">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b5">l</font> being   <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Olive" title="b4">k</font>,<font color="Maroon" title="c1">Al</font><br/>  for <font color="Olive" title="b6">P</font> being   <a href="qc_lang1.html#NM8" title="QC_LANG1:NM.8">QC-pred_symbol</a> of <font color="Olive" title="b4">k</font>,<font color="Maroon" title="c1">Al</font> holds <br/> ( <font color="Maroon">S<sub>1</sub></font>[ <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">VERUM</a> <font color="Maroon" title="c1">Al</font>] &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b6">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Olive" title="b5">l</font>] &amp; ( <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">r</font>] implies <font color="Maroon">S<sub>1</sub></font>[ <a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <font color="Olive" title="b1">r</font>] ) &amp; ( <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">r</font>] &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b2">s</font>] implies <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">r</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Olive" title="b2">s</font>] ) &amp; ( <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">r</font>] implies <font color="Maroon">S<sub>1</sub></font>[ <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Olive" title="b3">x</font>,<font color="Olive" title="b1">r</font>)] ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="substut2.html#T15" target="_self" onmouseover="rs('substut2/T15')" onmouseout="rh()">Th15</a>, <a class="ref" href="substut2.html#T18" target="_self" onmouseover="rs('substut2/T18')" onmouseout="rh()">Th18</a>, <a class="ref" href="substut2.html#T21" target="_self" onmouseover="rs('substut2/T21')" onmouseout="rh()">Th21</a>, <a class="ref" href="substut2.html#T23" target="_self" onmouseover="rs('substut2/T23')" onmouseout="rh()">Th23</a>, <a class="ref" href="substut2.html#T24" target="_self" onmouseover="rs('substut2/T24')" onmouseout="rh()">Th24</a></span>;<br/>
<span class="kw">thus </span><a NAME="E2:36"/>
 for <font color="Olive" title="b1">r</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">Al</font> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">r</font>]
 <span class="kw">from</span> <span class="lab"><a class="ref" href="cqc_lang.html#S1" onmouseover="rs('cqc_lang/S1')" onmouseout="rh()">CQC_LANG:sch 1</a>(<a class="txt" href="#E1:36"><span class="lab"><font color="Green" title="E21">A1</font></span></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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