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<b>let </b><font color="Maroon">x</font> be   <a href="qc_lang1.html#NM3">bound_QC-variable</a>;<br/><b>let </b><font color="Maroon">p</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> ;<br/>



<a NAME="E1:46"/>
 ex <font color="Olive">F</font> being  <a href="funct_2.html#NM1">Function</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> , <a href="qc_lang1.html#K8">QC-WFF</a>  st <br/>( <font color="Maroon">p</font> <a href="cqc_lang.html#K17" target="_self">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p</font> &amp; ( for <font color="Olive">q</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a>  holds <br/> ( <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <a href="cqc_lang.html#K9" target="_self">VERUM</a>  <a href="hidden.html#R1">=</a>  <a href="cqc_lang.html#K9" target="_self">VERUM</a>  &amp; ( <font color="Olive">q</font> is <a href="qc_lang1.html#V2">atomic</a> implies <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <font color="Olive">q</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K15">the_pred_symbol_of</a> <font color="Olive">q</font></span>)</span> <a href="qc_lang1.html#K9">!</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K4" target="_self">Subst</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K16">the_arguments_of</a> <font color="Olive">q</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qc_lang3.html#K3">a.</a> 0</span>)</span> <a href="cqc_lang.html#K6" target="_self">.--&gt;</a> <font color="Maroon">x</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive">q</font> is <a href="qc_lang1.html#V3">negative</a> implies <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <font color="Olive">q</font> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K12">'not'</a> <span class="p1">(<span class="default"><font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K17">the_argument_of</a> <font color="Olive">q</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive">q</font> is <a href="qc_lang1.html#V4">conjunctive</a> implies <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <font color="Olive">q</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K18">the_left_argument_of</a> <font color="Olive">q</font></span>)</span></span>)</span> <a href="qc_lang1.html#K13">'&amp;'</a> <span class="p1">(<span class="default"><font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K19">the_right_argument_of</a> <font color="Olive">q</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive">q</font> is <a href="qc_lang1.html#V5">universal</a> implies <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <font color="Olive">q</font> <a href="hidden.html#R1">=</a>  <a href="cqc_lang.html#K2" target="_self">IFEQ</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K20">bound_in</a> <font color="Olive">q</font></span>)</span>,<font color="Maroon">x</font>,<font color="Olive">q</font>,<span class="p1">(<span class="default"><a href="qc_lang1.html#K14">All</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K20">bound_in</a> <font color="Olive">q</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K21">the_scope_of</a> <font color="Olive">q</font></span>)</span></span>)</span></span>)</span> ) ) ) )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:46"/>
( <font color="Maroon">p</font> is <a href="qc_lang1.html#V2">atomic</a> implies <font color="Maroon">p</font> <a href="cqc_lang.html#K17" target="_self">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K15">the_pred_symbol_of</a> <font color="Maroon">p</font></span>)</span> <a href="qc_lang1.html#K9">!</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K4" target="_self">Subst</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K16">the_arguments_of</a> <font color="Maroon">p</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qc_lang3.html#K3">a.</a> 0</span>)</span> <a href="cqc_lang.html#K6" target="_self">.--&gt;</a> <font color="Maroon">x</font></span>)</span></span>)</span> )
 ;<br/>


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