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<span class="kw">let </span><font color="Maroon" title="c1">H</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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">H</font> is  <a href="qc_lang2.html#V1" title="QC_LANG2:attr.1">disjunctive</a>  implies ( <font color="Maroon" title="c1">H</font> is  <a href="qc_lang2.html#V2" title="QC_LANG2:attr.2">conditional</a>  &amp; <font color="Maroon" title="c1">H</font> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  &amp;  <a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <font color="Maroon" title="c1">H</font> is  <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a>  &amp;  <a href="qc_lang1.html#K18" title="QC_LANG1:func.18">the_left_argument_of</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="c1">H</font></span>)</span> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  &amp;  <a href="qc_lang1.html#K19" title="QC_LANG1:func.19">the_right_argument_of</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="c1">H</font></span>)</span> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  ) )</span><br/>

<span class="kw">given </span><font color="Maroon" title="c2">F</font>, <font color="Maroon" title="c3">G</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> <span class="kw"> such that </span><a NAME="E2:30"/><span class="lab"><font color="Green" title="E17">A1</font></span>: 
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">F</font> <a href="qc_lang2.html#K3" title="QC_LANG2:func.3">'or'</a> <font color="Maroon" title="c3">G</font>
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="qc_lang2.html#D10" target="_self" title="QC_LANG2:def.10">QC_LANG2:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">H</font> is  <a href="qc_lang2.html#V2" title="QC_LANG2:attr.2">conditional</a>  &amp; <font color="Maroon" title="c1">H</font> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  &amp;  <a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <font color="Maroon" title="c1">H</font> is  <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a>  &amp;  <a href="qc_lang1.html#K18" title="QC_LANG1:func.18">the_left_argument_of</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="c1">H</font></span>)</span> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  &amp;  <a href="qc_lang1.html#K19" title="QC_LANG1:func.19">the_right_argument_of</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="c1">H</font></span>)</span> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  )</span><br/>

<a NAME="E3:30"/>
<font color="Maroon" title="c2">F</font> <a href="qc_lang2.html#K3" title="QC_LANG2:func.3">'or'</a> <font color="Maroon" title="c3">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <font color="Maroon" title="c3">G</font>
 
;<br/>
<span class="kw">hence </span><a NAME="E4:30"/>
<font color="Maroon" title="c1">H</font> is  <a href="qc_lang2.html#V2" title="QC_LANG2:attr.2">conditional</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:30"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="qc_lang2.html#D11" target="_self" title="QC_LANG2:def.11">Def11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">H</font> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  &amp;  <a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <font color="Maroon" title="c1">H</font> is  <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a>  &amp;  <a href="qc_lang1.html#K18" title="QC_LANG1:func.18">the_left_argument_of</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="c1">H</font></span>)</span> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  &amp;  <a href="qc_lang1.html#K19" title="QC_LANG1:func.19">the_right_argument_of</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="c1">H</font></span>)</span> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E5:30"/>
<font color="Maroon" title="c1">H</font> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:30"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="qc_lang1.html#D17" title="QC_LANG1:def.17">QC_LANG1:def 17</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <font color="Maroon" title="c1">H</font> is  <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a>  &amp;  <a href="qc_lang1.html#K18" title="QC_LANG1:func.18">the_left_argument_of</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="c1">H</font></span>)</span> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  &amp;  <a href="qc_lang1.html#K19" title="QC_LANG1:func.19">the_right_argument_of</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="c1">H</font></span>)</span> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  )</span><br/>

<a NAME="E6:30"/><span class="lab"><font color="Green" title="E18">A2</font></span>: 
 <a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <font color="Maroon" title="c3">G</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:30"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="qc_lang2.html#T1" target="_self" title="QC_LANG2:th.1">Th2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:30"/>
 <a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <font color="Maroon" title="c1">H</font> is  <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#D18" title="QC_LANG1:def.18">QC_LANG1:def 18</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="qc_lang1.html#K18" title="QC_LANG1:func.18">the_left_argument_of</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="c1">H</font></span>)</span> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  &amp;  <a href="qc_lang1.html#K19" title="QC_LANG1:func.19">the_right_argument_of</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="c1">H</font></span>)</span> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  )</span><br/>

<a NAME="E8:30"/>
(  <a href="qc_lang1.html#K18" title="QC_LANG1:func.18">the_left_argument_of</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="c1">H</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <font color="Maroon" title="c2">F</font> &amp;  <a href="qc_lang1.html#K19" title="QC_LANG1:func.19">the_right_argument_of</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="c1">H</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <font color="Maroon" title="c3">G</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:30"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="ref" href="qc_lang2.html#T4" target="_self" title="QC_LANG2:th.4">Th5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:30"/>
(  <a href="qc_lang1.html#K18" title="QC_LANG1:func.18">the_left_argument_of</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="c1">H</font></span>)</span> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  &amp;  <a href="qc_lang1.html#K19" title="QC_LANG1:func.19">the_right_argument_of</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="c1">H</font></span>)</span> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#D17" title="QC_LANG1:def.17">QC_LANG1:def 17</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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