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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="Red">::  thesis: </font></span></a><span class="hide"> not <font color="Maroon" title="c1">H</font> <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a>  <a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a> </span><br/>

<div><span class="lab"><font color="Green" title="E19">A1</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="56_1"><span class="kw">now </span></a><div class="add"><span class="kw">given </span><font color="Maroon" title="c2">H1</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="E2:56_1"/><span class="lab"><font color="Green" title="E20">A2</font></span>: 
(  <a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</a> <font color="Maroon" title="c2">H1</font> or  <a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H1</font> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</a> <font color="Maroon" title="c1">H</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E3:56_1"/>
( <font color="Maroon" title="c1">H</font> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</a> <font color="Maroon" title="c2">H1</font> is  <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a>  &amp; <font color="Maroon" title="c2">H1</font> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</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#D19" title="QC_LANG1:def.19">QC_LANG1:def 19</a></span>;<br/><span class="kw">hence </span><a NAME="E4:56_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:56_1"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="ref" href="qc_lang1.html#T49" title="QC_LANG1:th.49">QC_LANG1:49</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/></div><span class="kw">end;</span></div>
<a NAME="E2:56"/>
 <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <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="ref" href="qc_lang1.html#D18" title="QC_LANG1:def.18">QC_LANG1:def 18</a></span>;<br/>
<a NAME="E3:56"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A3</font></span>: 
<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"><a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <font color="Maroon" title="c1">H</font></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="qc_lang1.html#T49" title="QC_LANG1:th.49">QC_LANG1:49</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:56"/>
<font color="Maroon" title="c1">H</font> <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a>  <a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c2">z</font> being   <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a><span class="kw"> such that </span><br/><a NAME="E6:56"/><span class="lab"><font color="Green" title="E21">A4</font></span>: 
 <a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> <font color="Maroon" title="c2">z</font>,<font color="Maroon" title="c1">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:56"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="txt" href="#E1:56"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="ref" href="qc_lang2.html#D20" target="_self" title="QC_LANG2:def.20">Def20</a>, <a class="ref" href="qc_lang1.html#T49" title="QC_LANG1:th.49">QC_LANG1:49</a></span>;<br/>
<a NAME="E7:56"/>
 <a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> <font color="Maroon" title="c2">z</font>,<font color="Maroon" title="c1">H</font> is  <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#D20" title="QC_LANG1:def.20">QC_LANG1:def 20</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:56"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:56"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="ref" href="qc_lang1.html#T49" title="QC_LANG1:th.49">QC_LANG1:49</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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