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<b>let </b><font color="Maroon" title="c1">p</font> be   <a href="qc_lang1.html#NM8" title="QC_LANG1:NM.8">QC-formula</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">p</font> is <a href="qc_lang2.html#V1" title="QC_LANG2:attr.1">disjunctive</a> implies  <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><a href="qc_lang2.html#K10" title="QC_LANG2:func.10">the_left_disjunct_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><a href="qc_lang2.html#K11" title="QC_LANG2:func.11">the_right_disjunct_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> )</span><br/>

<b>assume </b><a NAME="E1:20"/>
<font color="Maroon" title="c1">p</font> is <a href="qc_lang2.html#V1" title="QC_LANG2:attr.1">disjunctive</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><a href="qc_lang2.html#K10" title="QC_LANG2:func.10">the_left_disjunct_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><a href="qc_lang2.html#K11" title="QC_LANG2:func.11">the_right_disjunct_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span></span><br/>

<a NAME="E2:20"/><b>then </b><i><font color="Green" title="E12">A1</font></i>: 
<font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="qc_lang2.html#K10" title="QC_LANG2:func.10">the_left_disjunct_of</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="qc_lang2.html#K3" title="QC_LANG2:func.3">'or'</a> <span class="p1">(<span class="default"><a href="qc_lang2.html#K11" title="QC_LANG2:func.11">the_right_disjunct_of</a> <font color="Maroon" title="c1">p</font></span>)</span>
 
<b>by </b><i><a class="ref" href="qc_lang2.html#T53" title="QC_LANG2:th.53">QC_LANG2:53</a></i>;<br/>
<b>set </b><font color="Maroon" title="c2">p1</font> =  <a href="qc_lang2.html#K10" title="QC_LANG2:func.10">the_left_disjunct_of</a> <font color="Maroon" title="c1">p</font>;<br/>
<b>set </b><font color="Maroon" title="c3">p2</font> =  <a href="qc_lang2.html#K11" title="QC_LANG2:func.11">the_right_disjunct_of</a> <font color="Maroon" title="c1">p</font>;<br/>
<a NAME="E3:20"/>
<font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <span class="p3">(<span class="default"><a href="qc_lang2.html#K10" title="QC_LANG2:func.10">the_left_disjunct_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <span class="p3">(<span class="default"><a href="qc_lang2.html#K11" title="QC_LANG2:func.11">the_right_disjunct_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="qc_lang3.html#E2:20"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="qc_lang2.html#D3" title="QC_LANG2:def.3">QC_LANG2:def 3</a></i>;<br/>
<b>then </b> <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font> = 
 <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <span class="p3">(<span class="default"><a href="qc_lang2.html#K10" title="QC_LANG2:func.10">the_left_disjunct_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <span class="p3">(<span class="default"><a href="qc_lang2.html#K11" title="QC_LANG2:func.11">the_right_disjunct_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="qc_lang3.html#T11" target="_self" title="QC_LANG3:th.11">Th11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <span class="p3">(<span class="default"><a href="qc_lang2.html#K10" title="QC_LANG2:func.10">the_left_disjunct_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <span class="p3">(<span class="default"><a href="qc_lang2.html#K11" title="QC_LANG2:func.11">the_right_disjunct_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="qc_lang3.html#T14" target="_self" title="QC_LANG3:th.14">Th14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><a href="qc_lang2.html#K10" title="QC_LANG2:func.10">the_left_disjunct_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <span class="p3">(<span class="default"><a href="qc_lang2.html#K11" title="QC_LANG2:func.11">the_right_disjunct_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="qc_lang3.html#T11" target="_self" title="QC_LANG3:th.11">Th11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><a href="qc_lang2.html#K10" title="QC_LANG2:func.10">the_left_disjunct_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><a href="qc_lang2.html#K11" title="QC_LANG2:func.11">the_right_disjunct_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="qc_lang3.html#T11" target="_self" title="QC_LANG3:th.11">Th11</a></i>
;<br/>
<b>hence </b><a NAME="E5:20"/>
 <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><a href="qc_lang2.html#K10" title="QC_LANG2:func.10">the_left_disjunct_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><a href="qc_lang2.html#K11" title="QC_LANG2:func.11">the_right_disjunct_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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