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<span class="kw">let </span><font color="Maroon" title="c1">H</font>, <font color="Maroon" title="c2">G</font>, <font color="Maroon" title="c3">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> <a href="zf_lang.html#R1" title="ZF_LANG:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c2">G</font> or <font color="Maroon" title="c1">H</font> <a href="zf_lang.html#R3" title="ZF_LANG:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c2">G</font> or <font color="Maroon" title="c1">H</font> <a href="zf_lang.html#R2" title="ZF_LANG:pred.2">is_subformula_of</a> <font color="Maroon" title="c2">G</font> ) &amp; <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <font color="Maroon" title="c3">F</font> implies <font color="Maroon" title="c1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <font color="Maroon" title="c3">F</font> )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:108"/><span class="lab"><font color="Green" title="E83">A1</font></span>: 
( <font color="Maroon" title="c1">H</font> <a href="zf_lang.html#R1" title="ZF_LANG:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c2">G</font> or <font color="Maroon" title="c1">H</font> <a href="zf_lang.html#R3" title="ZF_LANG:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c2">G</font> or <font color="Maroon" title="c1">H</font> <a href="zf_lang.html#R2" title="ZF_LANG:pred.2">is_subformula_of</a> <font color="Maroon" title="c2">G</font> )
 <span class="kw">and </span><br/><a NAME="E2:108"/><span class="lab"><font color="Green" title="E84">A2</font></span>: 
<font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <font color="Maroon" title="c3">F</font>
 ; <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> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <font color="Maroon" title="c3">F</font></span><br/>

<a NAME="E3:108"/>
( <font color="Maroon" title="c1">H</font> <a href="zf_lang.html#R3" title="ZF_LANG:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c2">G</font> or <font color="Maroon" title="c1">H</font> <a href="zf_lang.html#R2" title="ZF_LANG:pred.2">is_subformula_of</a> <font color="Maroon" title="c2">G</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:108"><span class="lab"><font color="Green" title="E83">A1</font></span></a>, <a class="ref" href="zf_lang.html#T61" target="_self" title="ZF_LANG:th.61">Th82</a></span>;<br/>
<a NAME="E4:108"/><span class="kw">then </span><span class="lab"><font color="Green" title="E85">A3</font></span>: 
<font color="Maroon" title="c1">H</font> <a href="zf_lang.html#R2" title="ZF_LANG:pred.2">is_subformula_of</a> <font color="Maroon" title="c2">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang.html#D41" target="_self" title="ZF_LANG:def.41">Def41</a></span>;<br/>
<a NAME="E5:108"/>
<font color="Maroon" title="c2">G</font> <a href="zf_lang.html#R2" title="ZF_LANG:pred.2">is_subformula_of</a> <font color="Maroon" title="c3">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:108"><span class="lab"><font color="Green" title="E84">A2</font></span></a>, <a class="ref" href="zf_lang.html#T78" target="_self" title="ZF_LANG:th.78">Th100</a></span>;<br/>
<a NAME="E6:108"/><span class="kw">then </span>
<font color="Maroon" title="c1">H</font> <a href="zf_lang.html#R2" title="ZF_LANG:pred.2">is_subformula_of</a> <font color="Maroon" title="c3">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:108"><span class="lab"><font color="Green" title="E85">A3</font></span></a>, <a class="ref" href="zf_lang.html#T65" target="_self" title="ZF_LANG:th.65">Th86</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:108"/>
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <font color="Maroon" title="c3">F</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang.html#D42" target="_self" title="ZF_LANG:def.42">Def42</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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