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<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="subset_1.html#M1">Element</a> of  <a href="substut1.html#K16" target="_self">QC-Sub-WFF</a> ) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a>  = <span class="p1">(<span class="default"><a href="qc_lang1.html#K15">the_pred_symbol_of</a> <span class="p2">(<span class="default"><font color="Maroon">a<sub>1</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span> <a href="qc_lang1.html#K9">!</a> <span class="p1">(<span class="default"><a href="substut1.html#K3" target="_self">CQC_Subst</a> <span class="p2">(<span class="default"><a href="substut1.html#K26" target="_self">Sub_the_arguments_of</a> <font color="Maroon">a<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">a<sub>1</sub></font> <a href="substut1.html#K19" target="_self">`2</a> </span>)</span></span>)</span>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>2</sub></font>(   <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> ) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a>  =  <a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">a<sub>1</sub></font>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>3</sub></font>(   <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> ,   <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> ) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a>  = <font color="Maroon">a<sub>1</sub></font> <a href="qc_lang1.html#K13">'&amp;'</a> <font color="Maroon">a<sub>2</sub></font>;<br/>
<b>let </b><font color="Maroon">F1</font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="substut1.html#K16" target="_self">QC-Sub-WFF</a> , <a href="qc_lang1.html#K8">QC-WFF</a> , <font color="Maroon">F2</font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="substut1.html#K16" target="_self">QC-Sub-WFF</a> , <a href="qc_lang1.html#K8">QC-WFF</a> ;<br/>

<b>assume </b><a NAME="E1:80"/>
for <font color="Olive">S</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="substut1.html#K16" target="_self">QC-Sub-WFF</a>  holds <br/> ( ( <font color="Olive">S</font> is <a href="substut1.html#V2" target="_self">Sub_VERUM</a> implies <font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <font color="Olive">S</font> <a href="hidden.html#R1">=</a>  <a href="cqc_lang.html#K9">VERUM</a>  ) &amp; ( <font color="Olive">S</font> is <a href="substut1.html#V4" target="_self">Sub_atomic</a> implies <font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <font color="Olive">S</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">S</font>) ) &amp; ( <font color="Olive">S</font> is <a href="substut1.html#V5" target="_self">Sub_negative</a> implies <font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <font color="Olive">S</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="substut1.html#K27" target="_self">Sub_the_argument_of</a> <font color="Olive">S</font></span>)</span>) ) &amp; ( <font color="Olive">S</font> is <a href="substut1.html#V6" target="_self">Sub_conjunctive</a> implies <font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <font color="Olive">S</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="substut1.html#K28" target="_self">Sub_the_left_argument_of</a> <font color="Olive">S</font></span>)</span>,<font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="substut1.html#K29" target="_self">Sub_the_right_argument_of</a> <font color="Olive">S</font></span>)</span>) ) &amp; ( <font color="Olive">S</font> is <a href="substut1.html#V7" target="_self">Sub_universal</a> implies <font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <font color="Olive">S</font> <a href="hidden.html#R1">=</a>  <a href="substut1.html#K36" target="_self">Quant</a> <font color="Olive">S</font>,<span class="p1">(<span class="default"><font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="substut1.html#K31" target="_self">Sub_the_scope_of</a> <font color="Olive">S</font></span>)</span></span>)</span> ) )
 ;<br/>

<a NAME="E2:80"/><b>then </b><i><font color="Green">E40</font></i>: 
for <font color="Olive">S</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="substut1.html#K16" target="_self">QC-Sub-WFF</a> <br/> for <font color="Olive">d1</font>, <font color="Olive">d2</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">S</font> is <a href="substut1.html#V2" target="_self">Sub_VERUM</a> implies <font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <font color="Olive">S</font> <a href="hidden.html#R1">=</a>  <a href="cqc_lang.html#K9">VERUM</a>  ) &amp; ( <font color="Olive">S</font> is <a href="substut1.html#V4" target="_self">Sub_atomic</a> implies <font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <font color="Olive">S</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">S</font>) ) &amp; ( <font color="Olive">S</font> is <a href="substut1.html#V5" target="_self">Sub_negative</a> &amp; <font color="Olive">d1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="substut1.html#K27" target="_self">Sub_the_argument_of</a> <font color="Olive">S</font></span>)</span> implies <font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <font color="Olive">S</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive">d1</font>) ) &amp; ( <font color="Olive">S</font> is <a href="substut1.html#V6" target="_self">Sub_conjunctive</a> &amp; <font color="Olive">d1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="substut1.html#K28" target="_self">Sub_the_left_argument_of</a> <font color="Olive">S</font></span>)</span> &amp; <font color="Olive">d2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="substut1.html#K29" target="_self">Sub_the_right_argument_of</a> <font color="Olive">S</font></span>)</span> implies <font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <font color="Olive">S</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Olive">d1</font>,<font color="Olive">d2</font>) ) &amp; ( <font color="Olive">S</font> is <a href="substut1.html#V7" target="_self">Sub_universal</a> &amp; <font color="Olive">d1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="substut1.html#K31" target="_self">Sub_the_scope_of</a> <font color="Olive">S</font></span>)</span> implies <font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <font color="Olive">S</font> <a href="hidden.html#R1">=</a>  <a href="substut1.html#K36" target="_self">Quant</a> <font color="Olive">S</font>,<font color="Olive">d1</font> ) )
 
;<br/>
<b>assume </b><a NAME="E3:80"/>
for <font color="Olive">S</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="substut1.html#K16" target="_self">QC-Sub-WFF</a>  holds <br/> ( ( <font color="Olive">S</font> is <a href="substut1.html#V2" target="_self">Sub_VERUM</a> implies <font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <font color="Olive">S</font> <a href="hidden.html#R1">=</a>  <a href="cqc_lang.html#K9">VERUM</a>  ) &amp; ( <font color="Olive">S</font> is <a href="substut1.html#V4" target="_self">Sub_atomic</a> implies <font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <font color="Olive">S</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">S</font>) ) &amp; ( <font color="Olive">S</font> is <a href="substut1.html#V5" target="_self">Sub_negative</a> implies <font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <font color="Olive">S</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="substut1.html#K27" target="_self">Sub_the_argument_of</a> <font color="Olive">S</font></span>)</span>) ) &amp; ( <font color="Olive">S</font> is <a href="substut1.html#V6" target="_self">Sub_conjunctive</a> implies <font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <font color="Olive">S</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="substut1.html#K28" target="_self">Sub_the_left_argument_of</a> <font color="Olive">S</font></span>)</span>,<font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="substut1.html#K29" target="_self">Sub_the_right_argument_of</a> <font color="Olive">S</font></span>)</span>) ) &amp; ( <font color="Olive">S</font> is <a href="substut1.html#V7" target="_self">Sub_universal</a> implies <font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <font color="Olive">S</font> <a href="hidden.html#R1">=</a>  <a href="substut1.html#K36" target="_self">Quant</a> <font color="Olive">S</font>,<span class="p1">(<span class="default"><font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="substut1.html#K31" target="_self">Sub_the_scope_of</a> <font color="Olive">S</font></span>)</span></span>)</span> ) )
 ;<br/>

<a NAME="E4:80"/><b>then </b><i><font color="Green">E43</font></i>: 
for <font color="Olive">S</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="substut1.html#K16" target="_self">QC-Sub-WFF</a> <br/> for <font color="Olive">d1</font>, <font color="Olive">d2</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">S</font> is <a href="substut1.html#V2" target="_self">Sub_VERUM</a> implies <font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <font color="Olive">S</font> <a href="hidden.html#R1">=</a>  <a href="cqc_lang.html#K9">VERUM</a>  ) &amp; ( <font color="Olive">S</font> is <a href="substut1.html#V4" target="_self">Sub_atomic</a> implies <font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <font color="Olive">S</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">S</font>) ) &amp; ( <font color="Olive">S</font> is <a href="substut1.html#V5" target="_self">Sub_negative</a> &amp; <font color="Olive">d1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="substut1.html#K27" target="_self">Sub_the_argument_of</a> <font color="Olive">S</font></span>)</span> implies <font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <font color="Olive">S</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive">d1</font>) ) &amp; ( <font color="Olive">S</font> is <a href="substut1.html#V6" target="_self">Sub_conjunctive</a> &amp; <font color="Olive">d1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="substut1.html#K28" target="_self">Sub_the_left_argument_of</a> <font color="Olive">S</font></span>)</span> &amp; <font color="Olive">d2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="substut1.html#K29" target="_self">Sub_the_right_argument_of</a> <font color="Olive">S</font></span>)</span> implies <font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <font color="Olive">S</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Olive">d1</font>,<font color="Olive">d2</font>) ) &amp; ( <font color="Olive">S</font> is <a href="substut1.html#V7" target="_self">Sub_universal</a> &amp; <font color="Olive">d1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="substut1.html#K31" target="_self">Sub_the_scope_of</a> <font color="Olive">S</font></span>)</span> implies <font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <font color="Olive">S</font> <a href="hidden.html#R1">=</a>  <a href="substut1.html#K36" target="_self">Quant</a> <font color="Olive">S</font>,<font color="Olive">d1</font> ) )
 
;<br/>
<b>thus </b><a NAME="E5:80"/>
<font color="Maroon">F1</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">F2</font>
 <b>from </b><i><a class="ref" href="substut1.html#S4" target="_self">SUBSTUT1:sch 4</a>(, );</i><br/>


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