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<span class="kw">let </span><font color="Maroon" title="c1">H</font> be   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">H</font> is  <a href="zf_lang.html#V11" title="ZF_LANG:attr.11">existential</a>  implies ( <font color="Maroon" title="c1">H</font> is  <a href="zf_lang.html#V4" title="ZF_LANG:attr.4">negative</a>  &amp;  <a href="zf_lang.html#K20" title="ZF_LANG:func.20">the_argument_of</a> <font color="Maroon" title="c1">H</font> is  <a href="zf_lang.html#V6" title="ZF_LANG:attr.6">universal</a>  &amp;  <a href="zf_lang.html#K24" title="ZF_LANG:func.24">the_scope_of</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K20" title="ZF_LANG:func.20">the_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span> is  <a href="zf_lang.html#V4" title="ZF_LANG:attr.4">negative</a>  ) )</span><br/>

<span class="kw">assume </span><a NAME="E1:31"/>
<font color="Maroon" title="c1">H</font> is  <a href="zf_lang.html#V11" title="ZF_LANG:attr.11">existential</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">H</font> is  <a href="zf_lang.html#V4" title="ZF_LANG:attr.4">negative</a>  &amp;  <a href="zf_lang.html#K20" title="ZF_LANG:func.20">the_argument_of</a> <font color="Maroon" title="c1">H</font> is  <a href="zf_lang.html#V6" title="ZF_LANG:attr.6">universal</a>  &amp;  <a href="zf_lang.html#K24" title="ZF_LANG:func.24">the_scope_of</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K20" title="ZF_LANG:func.20">the_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span> is  <a href="zf_lang.html#V4" title="ZF_LANG:attr.4">negative</a>  )</span><br/>

<a NAME="E2:31"/><span class="kw">then </span><span class="lab"><font color="Green" title="E10">A1</font></span>: 
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K23" title="ZF_LANG:func.23">bound_in</a> <font color="Maroon" title="c1">H</font></span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K24" title="ZF_LANG:func.24">the_scope_of</a> <font color="Maroon" title="c1">H</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang.html#T63" title="ZF_LANG:th.63">ZF_LANG:63</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:31"/>
<font color="Maroon" title="c1">H</font> is  <a href="zf_lang.html#V4" title="ZF_LANG:attr.4">negative</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang.html#T16" title="ZF_LANG:th.16">ZF_LANG:16</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="zf_lang.html#K20" title="ZF_LANG:func.20">the_argument_of</a> <font color="Maroon" title="c1">H</font> is  <a href="zf_lang.html#V6" title="ZF_LANG:attr.6">universal</a>  &amp;  <a href="zf_lang.html#K24" title="ZF_LANG:func.24">the_scope_of</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K20" title="ZF_LANG:func.20">the_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span> is  <a href="zf_lang.html#V4" title="ZF_LANG:attr.4">negative</a>  )</span><br/>

<a NAME="E4:31"/><span class="lab"><font color="Green" title="E11">A2</font></span>: 
 <a href="zf_lang.html#K20" title="ZF_LANG:func.20">the_argument_of</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K23" title="ZF_LANG:func.23">bound_in</a> <font color="Maroon" title="c1">H</font></span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K24" title="ZF_LANG:func.24">the_scope_of</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:31"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="zf_lang1.html#T3" target="_self" title="ZF_LANG1:th.3">Th3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:31"/>
 <a href="zf_lang.html#K20" title="ZF_LANG:func.20">the_argument_of</a> <font color="Maroon" title="c1">H</font> is  <a href="zf_lang.html#V6" title="ZF_LANG:attr.6">universal</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang.html#T16" title="ZF_LANG:th.16">ZF_LANG:16</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="zf_lang.html#K24" title="ZF_LANG:func.24">the_scope_of</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K20" title="ZF_LANG:func.20">the_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span> is  <a href="zf_lang.html#V4" title="ZF_LANG:attr.4">negative</a> </span><br/>

<a NAME="E6:31"/>
 <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K24" title="ZF_LANG:func.24">the_scope_of</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K24" title="ZF_LANG:func.24">the_scope_of</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K20" title="ZF_LANG:func.20">the_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:31"><span class="lab"><font color="Green" title="E11">A2</font></span></a>, <a class="ref" href="zf_lang1.html#T8" target="_self" title="ZF_LANG1:th.8">Th8</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:31"/>
 <a href="zf_lang.html#K24" title="ZF_LANG:func.24">the_scope_of</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K20" title="ZF_LANG:func.20">the_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span> is  <a href="zf_lang.html#V4" title="ZF_LANG:attr.4">negative</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang.html#T16" title="ZF_LANG:th.16">ZF_LANG:16</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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