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<span class="kw">let </span><font color="Maroon" title="c1">F</font>, <font color="Maroon" title="c2">G</font>, <font color="Maroon" title="c3">H</font> be   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-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">F</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a> <font color="Maroon" title="c2">G</font> &amp; <font color="Maroon" title="c2">G</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a> <font color="Maroon" title="c3">H</font> implies <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a> <font color="Maroon" title="c3">H</font> )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:69"/><span class="lab"><font color="Green" title="E67">A1</font></span>: 
<font color="Maroon" title="c1">F</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a> <font color="Maroon" title="c2">G</font>
 <span class="kw">and </span><br/><a NAME="E2:69"/><span class="lab"><font color="Green" title="E68">A2</font></span>: 
<font color="Maroon" title="c2">G</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a> <font color="Maroon" title="c3">H</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">F</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a> <font color="Maroon" title="c3">H</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:69_1"/>
<font color="Maroon" title="c1">F</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">G</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">F</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a> <font color="Maroon" title="c3">H</font></span><br/><a NAME="E2:69_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E69">A3</font></span>: 
<font color="Maroon" title="c1">F</font> <a href="modelc_2.html#R3" title="MODELC_2:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c2">G</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69"><span class="lab"><font color="Green" title="E67">A1</font></span></a>, <a class="ref" href="modelc_2.html#D23" target="_self" title="MODELC_2:def.23">Def23</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:69_1_1"/>
<font color="Maroon" title="c2">G</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">H</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">F</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a> <font color="Maroon" title="c3">H</font></span><br/><a NAME="E2:69_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">G</font> <a href="modelc_2.html#R3" title="MODELC_2:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c3">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:69"><span class="lab"><font color="Green" title="E68">A2</font></span></a>, <a class="ref" href="modelc_2.html#D23" target="_self" title="MODELC_2:def.23">Def23</a></span>;<br/><a NAME="E3:69_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c1">F</font> <a href="modelc_2.html#R3" title="MODELC_2:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c3">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:69_1"><span class="lab"><font color="Green" title="E69">A3</font></span></a>, <a class="ref" href="modelc_2.html#T34" target="_self" title="MODELC_2:th.34">Th34</a></span>;<br/><span class="kw">hence </span><a NAME="E4:69_1_1"/>
<font color="Maroon" title="c1">F</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a> <font color="Maroon" title="c3">H</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D23" target="_self" title="MODELC_2:def.23">Def23</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">hence </span><a NAME="E4:69_1"/>
<font color="Maroon" title="c1">F</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a> <font color="Maroon" title="c3">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69"><span class="lab"><font color="Green" title="E67">A1</font></span></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">hence </span><a NAME="E4:69"/>
<font color="Maroon" title="c1">F</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a> <font color="Maroon" title="c3">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:69"><span class="lab"><font color="Green" title="E68">A2</font></span></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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