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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="zf_lang.html#NM1">Variable</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="zf_lang.html#NM2">ZF-formula</a>;<br/>





<b>thus </b><a NAME="E1:71"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="zf_lang.html#R1" target="_self">is_immediate_constituent_of</a>  <a href="zf_lang.html#K8" target="_self">All</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> implies <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:71_1"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="zf_lang.html#R1" target="_self">is_immediate_constituent_of</a>  <a href="zf_lang.html#K8" target="_self">All</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<div><i><font color="Green">E60</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="71_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:71_1_1"/><i><font color="Green">E61</font></i>: 
 <a href="zf_lang.html#K8" target="_self">All</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="zf_lang.html#K6" target="_self">'not'</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><a NAME="E2:71_1_1"/>
( <span class="p1">(<span class="default"><a href="zf_lang.html#K8" target="_self">All</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 4 &amp; <span class="p1">(<span class="default"><a href="zf_lang.html#K6" target="_self">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 2 )
 <b>by </b><i><a class="ref" href="zf_lang.html#T32" target="_self">Th32</a>, <a class="ref" href="zf_lang.html#T34" target="_self">Th34</a></i>;<br/><b>hence </b><a NAME="E3:71_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="zf_lang.html#E1:71_1_1"><i><font color="Green">E61</font></i></a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_1_2"><b>now </b></a><div class="add"><b>given </b><font color="Maroon">c<sub>4</sub></font> being   <a href="zf_lang.html#NM2">ZF-formula</a><b> such that </b><a NAME="E1:71_1_2"/><i><font color="Green">E61</font></i>: 
(  <a href="zf_lang.html#K8" target="_self">All</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="zf_lang.html#K7" target="_self">'&amp;'</a> <font color="Maroon">c<sub>4</sub></font> or  <a href="zf_lang.html#K8" target="_self">All</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="zf_lang.html#K7" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/><a NAME="E2:71_1_2"/>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="zf_lang.html#K7" target="_self">'&amp;'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 3 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="zf_lang.html#K7" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 3 &amp; <span class="p1">(<span class="default"><a href="zf_lang.html#K8" target="_self">All</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 4 )
 <b>by </b><i><a class="ref" href="zf_lang.html#T33" target="_self">Th33</a>, <a class="ref" href="zf_lang.html#T34" target="_self">Th34</a></i>;<br/><b>hence </b><a NAME="E3:71_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="zf_lang.html#E1:71_1_2"><i><font color="Green">E61</font></i></a></i>;<br/></div><b>end;</b></div>
<a NAME="E4:71_1"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="zf_lang.html#NM1">Variable</a> st  <a href="zf_lang.html#K8" target="_self">All</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="zf_lang.html#K8" target="_self">All</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="zf_lang.html#E1:71_1"><i><font color="Green">E59</font></i></a>, <a class="txt" href="zf_lang.html#E2:71_1"><i><font color="Green">E60</font></i></a>, <a class="ref" href="zf_lang.html#D39" target="_self">Def39</a></i>;<br/>
<b>hence </b><a NAME="E5:71_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="zf_lang.html#T12" target="_self">Th12</a></i>;<br/>


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

<b>thus </b><a NAME="E2:71"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> implies <font color="Maroon">c<sub>2</sub></font> <a href="zf_lang.html#R1" target="_self">is_immediate_constituent_of</a>  <a href="zf_lang.html#K8" target="_self">All</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="ref" href="zf_lang.html#D39" target="_self">Def39</a></i>;<br/>


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