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<span class="kw">let </span><font color="Maroon" title="c1">H</font>, <font color="Maroon" title="c2">F</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="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">H</font> is  <a href="zf_lang.html#V7" title="ZF_LANG:attr.7">atomic</a>  implies  not <font color="Maroon" title="c2">F</font> <a href="zf_lang.html#R1" title="ZF_LANG:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c1">H</font> )</span><br/>



<div><span class="lab"><font color="Green" title="E57">A1</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="71_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:71_1"/>
<font color="Maroon" title="c1">H</font> is  <a href="zf_lang.html#V2" title="ZF_LANG:attr.2">being_equality</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">H</font> is  <a href="zf_lang.html#V7" title="ZF_LANG:attr.7">atomic</a>  implies  not <font color="Maroon" title="c2">F</font> <a href="zf_lang.html#R1" title="ZF_LANG:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c1">H</font> )</span><br/><a NAME="E2:71_1"/><span class="kw">then </span>
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K18" title="ZF_LANG:func.18">Var1</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K19" title="ZF_LANG:func.19">Var2</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#T36" target="_self" title="ZF_LANG:th.36">Th53</a></span>;<br/><span class="kw">hence </span><a NAME="E3:71_1"/>
( <font color="Maroon" title="c1">H</font> is  <a href="zf_lang.html#V7" title="ZF_LANG:attr.7">atomic</a>  implies  not <font color="Maroon" title="c2">F</font> <a href="zf_lang.html#R1" title="ZF_LANG:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c1">H</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang.html#T50" target="_self" title="ZF_LANG:th.50">Th69</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E58">A2</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="71_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:71_2"/>
<font color="Maroon" title="c1">H</font> is  <a href="zf_lang.html#V3" title="ZF_LANG:attr.3">being_membership</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">H</font> is  <a href="zf_lang.html#V7" title="ZF_LANG:attr.7">atomic</a>  implies  not <font color="Maroon" title="c2">F</font> <a href="zf_lang.html#R1" title="ZF_LANG:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c1">H</font> )</span><br/><a NAME="E2:71_2"/><span class="kw">then </span>
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K18" title="ZF_LANG:func.18">Var1</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="zf_lang.html#K5" title="ZF_LANG:func.5">'in'</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K19" title="ZF_LANG:func.19">Var2</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#T37" target="_self" title="ZF_LANG:th.37">Th54</a></span>;<br/><span class="kw">hence </span><a NAME="E3:71_2"/>
( <font color="Maroon" title="c1">H</font> is  <a href="zf_lang.html#V7" title="ZF_LANG:attr.7">atomic</a>  implies  not <font color="Maroon" title="c2">F</font> <a href="zf_lang.html#R1" title="ZF_LANG:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c1">H</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang.html#T51" target="_self" title="ZF_LANG:th.51">Th70</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E3:71"/>
<font color="Maroon" title="c1">H</font> is  <a href="zf_lang.html#V7" title="ZF_LANG:attr.7">atomic</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c2">F</font> <a href="zf_lang.html#R1" title="ZF_LANG:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c1">H</font></span><br/>

<span class="kw">hence </span><a NAME="E4:71"/>
 not <font color="Maroon" title="c2">F</font> <a href="zf_lang.html#R1" title="ZF_LANG:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c1">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:71"><span class="lab"><font color="Green" title="E57">A1</font></span></a>, <a class="txt" href="#E2:71"><span class="lab"><font color="Green" title="E58">A2</font></span></a>, <a class="ref" href="zf_lang.html#D15" target="_self" title="ZF_LANG:def.15">Def15</a></span>; <a class="txt" 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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