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<b>let </b><font color="Maroon" title="c1">F</font>, <font color="Maroon" title="c2">G</font> be   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="zf_lang.html#R3" title="ZF_LANG:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">'or'</a> <font color="Maroon" title="c2">G</font> &amp;  <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#R3" title="ZF_LANG:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">'or'</a> <font color="Maroon" title="c2">G</font> &amp;  <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c2">G</font> <a href="zf_lang.html#R3" title="ZF_LANG:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">'or'</a> <font color="Maroon" title="c2">G</font> &amp; <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#R3" title="ZF_LANG:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">'or'</a> <font color="Maroon" title="c2">G</font> &amp; <font color="Maroon" title="c2">G</font> <a href="zf_lang.html#R3" title="ZF_LANG:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">'or'</a> <font color="Maroon" title="c2">G</font> )</span><br/>



<a NAME="E1:40"/>
<span class="p1">(<span class="default"><a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="zf_lang.html#R1" title="ZF_LANG:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">'or'</a> <font color="Maroon" title="c2">G</font>
 
<b>by </b><i><a class="ref" href="zf_lang.html#D39" title="ZF_LANG:def.39">ZF_LANG:def 39</a></i>;<br/>
<b>hence </b><a NAME="E2:40"/><i><font color="Green" title="E12">A1</font></i>: 
<span class="p1">(<span class="default"><a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="zf_lang.html#R3" title="ZF_LANG:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">'or'</a> <font color="Maroon" title="c2">G</font>
 <b>by </b><i><a class="ref" href="zf_lang.html#T82" title="ZF_LANG:th.82">ZF_LANG:82</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#R3" title="ZF_LANG:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">'or'</a> <font color="Maroon" title="c2">G</font> &amp;  <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c2">G</font> <a href="zf_lang.html#R3" title="ZF_LANG:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">'or'</a> <font color="Maroon" title="c2">G</font> &amp; <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#R3" title="ZF_LANG:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">'or'</a> <font color="Maroon" title="c2">G</font> &amp; <font color="Maroon" title="c2">G</font> <a href="zf_lang.html#R3" title="ZF_LANG:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">'or'</a> <font color="Maroon" title="c2">G</font> )</span><br/>

<a NAME="E3:40"/>
(  <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#R1" title="ZF_LANG:pred.1">is_immediate_constituent_of</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c2">G</font></span>)</span> &amp;  <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c2">G</font> <a href="zf_lang.html#R1" title="ZF_LANG:pred.1">is_immediate_constituent_of</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c2">G</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="zf_lang.html#D39" title="ZF_LANG:def.39">ZF_LANG:def 39</a></i>;<br/>
<b>hence </b><a NAME="E4:40"/><i><font color="Green" title="E13">A2</font></i>: 
(  <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#R3" title="ZF_LANG:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">'or'</a> <font color="Maroon" title="c2">G</font> &amp;  <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c2">G</font> <a href="zf_lang.html#R3" title="ZF_LANG:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">'or'</a> <font color="Maroon" title="c2">G</font> )
 <b>by </b><i><a class="txt" href="zf_lang1.html#E2:40"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="zf_lang1.html#T44" target="_self" title="ZF_LANG1:th.44">Th44</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#R3" title="ZF_LANG:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">'or'</a> <font color="Maroon" title="c2">G</font> &amp; <font color="Maroon" title="c2">G</font> <a href="zf_lang.html#R3" title="ZF_LANG:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">'or'</a> <font color="Maroon" title="c2">G</font> )</span><br/>

<a NAME="E5:40"/>
( <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#R1" title="ZF_LANG:pred.1">is_immediate_constituent_of</a>  <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c1">F</font> &amp; <font color="Maroon" title="c2">G</font> <a href="zf_lang.html#R1" title="ZF_LANG:pred.1">is_immediate_constituent_of</a>  <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c2">G</font> )
 
<b>by </b><i><a class="ref" href="zf_lang.html#D39" title="ZF_LANG:def.39">ZF_LANG:def 39</a></i>;<br/>
<b>hence </b><a NAME="E6:40"/>
( <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#R3" title="ZF_LANG:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">'or'</a> <font color="Maroon" title="c2">G</font> &amp; <font color="Maroon" title="c2">G</font> <a href="zf_lang.html#R3" title="ZF_LANG:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">'or'</a> <font color="Maroon" title="c2">G</font> )
 <b>by </b><i><a class="txt" href="zf_lang1.html#E4:40"><i><font color="Green" title="E13">A2</font></i></a>, <a class="ref" href="zf_lang1.html#T44" target="_self" title="ZF_LANG1:th.44">Th44</a></i>; <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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