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<b>let </b><font color="Maroon">S</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="substut1.html#K16" target="_self">QC-Sub-WFF</a> ;<br/>

<a NAME="E1:73"/>
( ( <font color="Maroon">S</font> is <a href="substut1.html#V2" target="_self">Sub_VERUM</a> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K10">@</a> <span class="p3">(<span class="default"><font color="Maroon">S</font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1</span>)</span> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R1">=</a> 0 ) &amp; ( <font color="Maroon">S</font> is <a href="substut1.html#V4" target="_self">Sub_atomic</a> implies  ex <font color="Olive">k</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <span class="p1">(<span class="default"><a href="qc_lang1.html#K10">@</a> <span class="p2">(<span class="default"><font color="Maroon">S</font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1 is   <a href="qc_lang1.html#NM6">QC-pred_symbol</a> of <font color="Olive">k</font> ) &amp; ( <font color="Maroon">S</font> is <a href="substut1.html#V5" target="_self">Sub_negative</a> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K10">@</a> <span class="p3">(<span class="default"><font color="Maroon">S</font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1</span>)</span> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R1">=</a> 1 ) &amp; ( <font color="Maroon">S</font> is <a href="substut1.html#V6" target="_self">Sub_conjunctive</a> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K10">@</a> <span class="p3">(<span class="default"><font color="Maroon">S</font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1</span>)</span> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R1">=</a> 2 ) &amp; ( <font color="Maroon">S</font> is <a href="substut1.html#V7" target="_self">Sub_universal</a> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K10">@</a> <span class="p3">(<span class="default"><font color="Maroon">S</font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1</span>)</span> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R1">=</a> 3 ) )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:73"/>
( not <!--HUMANRECFAILED-->( <font color="Maroon">S</font> is <a href="substut1.html#V4" target="_self">Sub_atomic</a> &amp; <font color="Maroon">S</font> is <a href="substut1.html#V5" target="_self">Sub_negative</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon">S</font> is <a href="substut1.html#V4" target="_self">Sub_atomic</a> &amp; <font color="Maroon">S</font> is <a href="substut1.html#V6" target="_self">Sub_conjunctive</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon">S</font> is <a href="substut1.html#V4" target="_self">Sub_atomic</a> &amp; <font color="Maroon">S</font> is <a href="substut1.html#V7" target="_self">Sub_universal</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon">S</font> is <a href="substut1.html#V5" target="_self">Sub_negative</a> &amp; <font color="Maroon">S</font> is <a href="substut1.html#V6" target="_self">Sub_conjunctive</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon">S</font> is <a href="substut1.html#V5" target="_self">Sub_negative</a> &amp; <font color="Maroon">S</font> is <a href="substut1.html#V7" target="_self">Sub_universal</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon">S</font> is <a href="substut1.html#V6" target="_self">Sub_conjunctive</a> &amp; <font color="Maroon">S</font> is <a href="substut1.html#V7" target="_self">Sub_universal</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon">S</font> is <a href="substut1.html#V2" target="_self">Sub_VERUM</a> &amp; <font color="Maroon">S</font> is <a href="substut1.html#V4" target="_self">Sub_atomic</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon">S</font> is <a href="substut1.html#V2" target="_self">Sub_VERUM</a> &amp; <font color="Maroon">S</font> is <a href="substut1.html#V5" target="_self">Sub_negative</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon">S</font> is <a href="substut1.html#V2" target="_self">Sub_VERUM</a> &amp; <font color="Maroon">S</font> is <a href="substut1.html#V6" target="_self">Sub_conjunctive</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon">S</font> is <a href="substut1.html#V2" target="_self">Sub_VERUM</a> &amp; <font color="Maroon">S</font> is <a href="substut1.html#V7" target="_self">Sub_universal</a> ) )
 <b>by </b><i/>;<br/>


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