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<span class="kw">let </span><font color="Maroon" title="c1">S</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V4" title="SUBSTUT1:attr.4">Sub_atomic</a>  &amp; <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V5" title="SUBSTUT1:attr.5">Sub_negative</a>  ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V4" title="SUBSTUT1:attr.4">Sub_atomic</a>  &amp; <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V6" title="SUBSTUT1:attr.6">Sub_conjunctive</a>  ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V4" title="SUBSTUT1:attr.4">Sub_atomic</a>  &amp; <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V7" title="SUBSTUT1:attr.7">Sub_universal</a>  ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V5" title="SUBSTUT1:attr.5">Sub_negative</a>  &amp; <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V6" title="SUBSTUT1:attr.6">Sub_conjunctive</a>  ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V5" title="SUBSTUT1:attr.5">Sub_negative</a>  &amp; <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V7" title="SUBSTUT1:attr.7">Sub_universal</a>  ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V6" title="SUBSTUT1:attr.6">Sub_conjunctive</a>  &amp; <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V7" title="SUBSTUT1:attr.7">Sub_universal</a>  ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V2" title="SUBSTUT1:attr.2">Sub_VERUM</a>  &amp; <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V4" title="SUBSTUT1:attr.4">Sub_atomic</a>  ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V2" title="SUBSTUT1:attr.2">Sub_VERUM</a>  &amp; <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V5" title="SUBSTUT1:attr.5">Sub_negative</a>  ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V2" title="SUBSTUT1:attr.2">Sub_VERUM</a>  &amp; <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V6" title="SUBSTUT1:attr.6">Sub_conjunctive</a>  ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V2" title="SUBSTUT1:attr.2">Sub_VERUM</a>  &amp; <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V7" title="SUBSTUT1:attr.7">Sub_universal</a>  ) )</span><br/>

<a NAME="E1:73"/><span class="lab"><font color="Green" title="E43">A1</font></span>: 
( <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V5" title="SUBSTUT1:attr.5">Sub_negative</a>  implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K10" title="QC_LANG1:func.10">@</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="substut1.html#T25" target="_self" title="SUBSTUT1:th.25">Th25</a></span>;<br/>
<a NAME="E2:73"/><span class="lab"><font color="Green" title="E44">A2</font></span>: 
( <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V6" title="SUBSTUT1:attr.6">Sub_conjunctive</a>  implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K10" title="QC_LANG1:func.10">@</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="substut1.html#T25" target="_self" title="SUBSTUT1:th.25">Th25</a></span>;<br/>
<a NAME="E3:73"/><span class="lab"><font color="Green" title="E45">A3</font></span>: 
( <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V7" title="SUBSTUT1:attr.7">Sub_universal</a>  implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K10" title="QC_LANG1:func.10">@</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="substut1.html#T25" target="_self" title="SUBSTUT1:th.25">Th25</a></span>;<br/>
<a NAME="E4:73"/>
( <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V2" title="SUBSTUT1:attr.2">Sub_VERUM</a>  implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K10" title="QC_LANG1:func.10">@</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="substut1.html#T25" target="_self" title="SUBSTUT1:th.25">Th25</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:73"/>
( not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V4" title="SUBSTUT1:attr.4">Sub_atomic</a>  &amp; <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V5" title="SUBSTUT1:attr.5">Sub_negative</a>  ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V4" title="SUBSTUT1:attr.4">Sub_atomic</a>  &amp; <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V6" title="SUBSTUT1:attr.6">Sub_conjunctive</a>  ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V4" title="SUBSTUT1:attr.4">Sub_atomic</a>  &amp; <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V7" title="SUBSTUT1:attr.7">Sub_universal</a>  ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V5" title="SUBSTUT1:attr.5">Sub_negative</a>  &amp; <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V6" title="SUBSTUT1:attr.6">Sub_conjunctive</a>  ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V5" title="SUBSTUT1:attr.5">Sub_negative</a>  &amp; <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V7" title="SUBSTUT1:attr.7">Sub_universal</a>  ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V6" title="SUBSTUT1:attr.6">Sub_conjunctive</a>  &amp; <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V7" title="SUBSTUT1:attr.7">Sub_universal</a>  ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V2" title="SUBSTUT1:attr.2">Sub_VERUM</a>  &amp; <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V4" title="SUBSTUT1:attr.4">Sub_atomic</a>  ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V2" title="SUBSTUT1:attr.2">Sub_VERUM</a>  &amp; <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V5" title="SUBSTUT1:attr.5">Sub_negative</a>  ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V2" title="SUBSTUT1:attr.2">Sub_VERUM</a>  &amp; <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V6" title="SUBSTUT1:attr.6">Sub_conjunctive</a>  ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V2" title="SUBSTUT1:attr.2">Sub_VERUM</a>  &amp; <font color="Maroon" title="c1">S</font> is  <a href="substut1.html#V7" title="SUBSTUT1:attr.7">Sub_universal</a>  ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:73"><span class="lab"><font color="Green" title="E43">A1</font></span></a>, <a class="txt" href="#E2:73"><span class="lab"><font color="Green" title="E44">A2</font></span></a>, <a class="txt" href="#E3:73"><span class="lab"><font color="Green" title="E45">A3</font></span></a>, <a class="ref" href="substut1.html#T26" target="_self" title="SUBSTUT1:th.26">Th26</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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