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<b>let </b><font color="Maroon" title="c1">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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">p</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a>   st <font color="Olive" title="b1">p</font> is <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a> holds <br/><font color="Olive" title="b1">p</font> <a href="cqc_lang.html#K14" title="CQC_LANG:func.14">.</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <font color="Olive" title="b1">p</font></span>)</span> <a href="cqc_lang.html#K14" title="CQC_LANG:func.14">.</a> <font color="Maroon" title="c1">x</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">p</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">p</font> is <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a> implies <font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K14" title="CQC_LANG:func.14">.</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="cqc_lang.html#K14" title="CQC_LANG:func.14">.</a> <font color="Maroon" title="c1">x</font></span>)</span> )</span><br/>



<b>consider </b><font color="Maroon" title="c3">F</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a> , <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a> <b> such that </b><br/><a NAME="E2:43"/><i><font color="Green" title="E23">A1</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K14" title="CQC_LANG:func.14">.</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">p</font>
 <b>and </b><br/><a NAME="E3:43"/><i><font color="Green" title="E24">A2</font></i>: 
for <font color="Olive" title="b1">q</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a>  holds <br/> ( <font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <a href="cqc_lang.html#K6" title="CQC_LANG:func.6">VERUM</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_lang.html#K6" title="CQC_LANG:func.6">VERUM</a>  &amp; ( <font color="Olive" title="b1">q</font> is <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a> implies <font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K15" title="QC_LANG1:func.15">the_pred_symbol_of</a> <font color="Olive" title="b1">q</font></span>)</span> <a href="qc_lang1.html#K9" title="QC_LANG1:func.9">!</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K1" title="CQC_LANG:func.1">Subst</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K16" title="QC_LANG1:func.16">the_arguments_of</a> <font color="Olive" title="b1">q</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qc_lang3.html#K3" title="QC_LANG3:func.3">a.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <font color="Maroon" title="c1">x</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive" title="b1">q</font> is <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a> implies <font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <font color="Olive" title="b1">q</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive" title="b1">q</font> is <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a> implies <font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K18" title="QC_LANG1:func.18">the_left_argument_of</a> <font color="Olive" title="b1">q</font></span>)</span></span>)</span> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K19" title="QC_LANG1:func.19">the_right_argument_of</a> <font color="Olive" title="b1">q</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive" title="b1">q</font> is <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a> implies <font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funcop_1.html#K15" title="FUNCOP_1:func.15">IFEQ</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K20" title="QC_LANG1:func.20">bound_in</a> <font color="Olive" title="b1">q</font></span>)</span>,<font color="Maroon" title="c1">x</font>,<font color="Olive" title="b1">q</font>,<span class="p1">(<span class="default"><a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K20" title="QC_LANG1:func.20">bound_in</a> <font color="Olive" title="b1">q</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K21" title="QC_LANG1:func.21">the_scope_of</a> <font color="Olive" title="b1">q</font></span>)</span></span>)</span></span>)</span> ) )
 <b>by </b><i><a class="ref" href="cqc_lang.html#D6" target="_self" title="CQC_LANG:def.6">Def6</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c4">G</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a> , <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a> <b> such that </b><br/><a NAME="E5:43"/><i><font color="Green" title="E25">A3</font></i>: 
<span class="p1">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="cqc_lang.html#K14" title="CQC_LANG:func.14">.</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <font color="Maroon" title="c2">p</font></span>)</span>
 <b>and </b><br/><a NAME="E6:43"/><i><font color="Green" title="E26">A4</font></i>: 
for <font color="Olive" title="b1">q</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a>  holds <br/> ( <font color="Maroon" title="c4">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <a href="cqc_lang.html#K6" title="CQC_LANG:func.6">VERUM</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_lang.html#K6" title="CQC_LANG:func.6">VERUM</a>  &amp; ( <font color="Olive" title="b1">q</font> is <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a> implies <font color="Maroon" title="c4">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K15" title="QC_LANG1:func.15">the_pred_symbol_of</a> <font color="Olive" title="b1">q</font></span>)</span> <a href="qc_lang1.html#K9" title="QC_LANG1:func.9">!</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K1" title="CQC_LANG:func.1">Subst</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K16" title="QC_LANG1:func.16">the_arguments_of</a> <font color="Olive" title="b1">q</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qc_lang3.html#K3" title="QC_LANG3:func.3">a.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <font color="Maroon" title="c1">x</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive" title="b1">q</font> is <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a> implies <font color="Maroon" title="c4">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <font color="Olive" title="b1">q</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive" title="b1">q</font> is <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a> implies <font color="Maroon" title="c4">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K18" title="QC_LANG1:func.18">the_left_argument_of</a> <font color="Olive" title="b1">q</font></span>)</span></span>)</span> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K19" title="QC_LANG1:func.19">the_right_argument_of</a> <font color="Olive" title="b1">q</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive" title="b1">q</font> is <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a> implies <font color="Maroon" title="c4">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funcop_1.html#K15" title="FUNCOP_1:func.15">IFEQ</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K20" title="QC_LANG1:func.20">bound_in</a> <font color="Olive" title="b1">q</font></span>)</span>,<font color="Maroon" title="c1">x</font>,<font color="Olive" title="b1">q</font>,<span class="p1">(<span class="default"><a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K20" title="QC_LANG1:func.20">bound_in</a> <font color="Olive" title="b1">q</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K21" title="QC_LANG1:func.21">the_scope_of</a> <font color="Olive" title="b1">q</font></span>)</span></span>)</span></span>)</span> ) )
 <b>by </b><i><a class="ref" href="cqc_lang.html#D6" target="_self" title="CQC_LANG:def.6">Def6</a></i>;<br/>
<a NAME="E7:43"/>
<font color="Maroon" title="c3">F</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">G</font>
 
<b>by </b><i><a class="txt" href="#E3:43"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="#E6:43"><i><font color="Green" title="E26">A4</font></i></a>, <a class="txt" href="cqc_lang.html#E31"><i><font color="Green" title="E17">Lm2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E8:43"/>
( <font color="Maroon" title="c2">p</font> is <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a> implies <font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K14" title="CQC_LANG:func.14">.</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="cqc_lang.html#K14" title="CQC_LANG:func.14">.</a> <font color="Maroon" title="c1">x</font></span>)</span> )
 <b>by </b><i><a class="txt" href="#E2:43"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="#E3:43"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="#E5:43"><i><font color="Green" title="E25">A3</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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