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<b>let </b><font color="Maroon" title="c1">F</font>, <font color="Maroon" title="c2">H</font> be   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>;<br/>



<b>thus </b><a NAME="E1:69"/>
( <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="c2">H</font> implies <font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:69_1"/>
<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="c2">H</font>
 ;<br/>

<a NAME="E2:69_1"/><b>then </b><i><font color="Green" title="E55">A1</font></i>: 
(  <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c2">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c1">F</font> or  ex <font color="Olive" title="b1">H1</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> st <br/>(  <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c2">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Olive" title="b1">H1</font> or  <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c2">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">H1</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c1">F</font> ) or  ex <font color="Olive" title="b1">x</font> being  <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a> st  <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c2">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> <font color="Olive" title="b1">x</font>,<font color="Maroon" title="c1">F</font> )
 
<b>by </b><i><a class="ref" href="zf_lang.html#D39" target="_self" title="ZF_LANG:def.39">Def39</a></i>;<br/>
<div><i><font color="Green" title="E56">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="69_1_1"><b>now </b></a><div class="add"><b>given </b><font color="Maroon" title="c3">H1</font> being   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a><b> such that </b><a NAME="E2:69_1_1"/><i><font color="Green" title="E57">A3</font></i>: 
(  <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c2">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c3">H1</font> or  <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c2">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H1</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c1">F</font> )
 ;<br/><a NAME="E3:69_1_1"/>
( <span class="p1">(<span class="default"><a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c2">H</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c3">H1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">H1</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 )
 <b>by </b><i><a class="ref" href="zf_lang.html#T33" target="_self" title="ZF_LANG:th.33">Th33</a>, <a class="ref" href="finseq_1.html#T58" title="FINSEQ_1:th.58">FINSEQ_1:58</a></i>;<br/><b>hence </b><a NAME="E4:69_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="zf_lang.html#E2:69_1_1"><i><font color="Green" title="E57">A3</font></i></a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_1_2"><b>now </b></a><div class="add"><b>given </b><font color="Maroon" title="c3">x</font> being   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a><b> such that </b><a NAME="E2:69_1_2"/><i><font color="Green" title="E57">A4</font></i>: 
 <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c2">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> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c1">F</font>
 ;<br/><a NAME="E3:69_1_2"/>
( <span class="p1">(<span class="default"><a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c2">H</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <span class="p1">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c1">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 )
 <b>by </b><i><a class="ref" href="zf_lang.html#T34" target="_self" title="ZF_LANG:th.34">Th34</a>, <a class="ref" href="finseq_1.html#T58" title="FINSEQ_1:th.58">FINSEQ_1:58</a></i>;<br/><b>hence </b><a NAME="E4:69_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="zf_lang.html#E2:69_1_2"><i><font color="Green" title="E57">A4</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:69_1"/>
<font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H</font>
 <b>by </b><i><a class="txt" href="zf_lang.html#E2:69_1"><i><font color="Green" title="E55">A1</font></i></a>, <a class="txt" href="zf_lang.html#E3:69_1"><i><font color="Green" title="E56">A2</font></i></a>, <a class="ref" href="finseq_1.html#T46" title="FINSEQ_1:th.46">FINSEQ_1:46</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:69"/>
( <font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H</font> implies <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="c2">H</font> )
 <b>by </b><i><a class="ref" href="zf_lang.html#D39" target="_self" title="ZF_LANG:def.39">Def39</a></i>;<br/>


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