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<span class="kw">let </span><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font> be   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">H</font> being   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>  holds  not <font color="Olive" title="b1">H</font> <a href="zf_lang.html#R1" title="ZF_LANG:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c1">x</font> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'in'</a> <font color="Maroon" title="c2">y</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">H</font> be   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c3">H</font> <a href="zf_lang.html#R1" title="ZF_LANG:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c1">x</font> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'in'</a> <font color="Maroon" title="c2">y</font></span><br/>





<span class="kw">assume </span><a NAME="E1:65"/>
<font color="Maroon" title="c3">H</font> <a href="zf_lang.html#R1" title="ZF_LANG:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c1">x</font> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'in'</a> <font color="Maroon" title="c2">y</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:65"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A1</font></span>: 
( <font color="Maroon" title="c1">x</font> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'in'</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K5" title="ZF_LANG:func.5">'not'</a> <font color="Maroon" title="c3">H</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/>( <font color="Maroon" title="c1">x</font> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'in'</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H</font> <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'&amp;'</a> <font color="Olive" title="b1">H1</font> or <font color="Maroon" title="c1">x</font> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'in'</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">H1</font> <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'&amp;'</a> <font color="Maroon" title="c3">H</font> ) or  ex <font color="Olive" title="b1">z</font> being   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a> st <font color="Maroon" title="c1">x</font> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'in'</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K7" title="ZF_LANG:func.7">All</a> (<font color="Olive" title="b1">z</font>,<font color="Maroon" title="c3">H</font>) )
 
;<br/>
<a NAME="E3:65"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'in'</a> <font color="Maroon" title="c2">y</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> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang.html#T15" target="_self" onmouseover="rs('zf_lang/T15')" onmouseout="rh()">Th15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:65"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:65"><span class="lab"><font color="Green" title="E43">A1</font></span></a>, <a class="ref" href="zf_lang.html#T16" target="_self" onmouseover="rs('zf_lang/T16')" onmouseout="rh()">Th16</a>, <a class="ref" href="zf_lang.html#T17" target="_self" onmouseover="rs('zf_lang/T17')" onmouseout="rh()">Th17</a>, <a class="ref" href="finseq_1.html#T41" onmouseover="rs('finseq_1/T41')" onmouseout="rh()">FINSEQ_1:41</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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