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<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="sheffer1.html#V10" title="SHEFFER1:attr.10">satisfying_Sheffer_1</a> <a href="sheffer1.html#V11" title="SHEFFER1:attr.11">satisfying_Sheffer_2</a> <a href="sheffer1.html#V12" title="SHEFFER1:attr.12">satisfying_Sheffer_3</a>  <a href="sheffer1.html#L1" title="SHEFFER1:struct.1">ShefferStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">z</font>, <font color="Olive" title="b2">w</font>, <font color="Olive" title="b3">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b3">x</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Olive" title="b3">x</font></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Olive" title="b2">w</font></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b1">z</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Olive" title="b1">z</font></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Olive" title="b2">w</font></span>)</span></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">w</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p3">(<span class="default"><font color="Olive" title="b3">x</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Olive" title="b1">z</font></span>)</span></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">w</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p3">(<span class="default"><font color="Olive" title="b3">x</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Olive" title="b1">z</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">w</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Olive" title="b2">w</font></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">w</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p3">(<span class="default"><font color="Olive" title="b3">x</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Olive" title="b1">z</font></span>)</span></span>)</span></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b3">x</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Olive" title="b1">z</font></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p3">(<span class="default"><font color="Olive" title="b3">x</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Olive" title="b1">z</font></span>)</span></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">w</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p3">(<span class="default"><font color="Olive" title="b3">x</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Olive" title="b1">z</font></span>)</span></span>)</span></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">z</font>, <font color="Maroon" title="c3">w</font>, <font color="Maroon" title="c4">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Maroon" title="c4">x</font></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Maroon" title="c3">w</font></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Maroon" title="c2">z</font></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Maroon" title="c3">w</font></span>)</span></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">w</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">w</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">w</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Maroon" title="c3">w</font></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">w</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Maroon" title="c2">z</font></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">w</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span></span>)</span></span><br/>







<a NAME="E1:98"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">w</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">w</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Maroon" title="c4">x</font></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Maroon" title="c3">w</font></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Maroon" title="c2">z</font></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Maroon" title="c3">w</font></span>)</span>
 
<b>by </b><i><a class="ref" href="sheffer1.html#D15" title="SHEFFER1:def.15">SHEFFER1:def 15</a></i>;<br/>
<b>hence </b><a NAME="E2:98"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Maroon" title="c4">x</font></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Maroon" title="c3">w</font></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Maroon" title="c2">z</font></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Maroon" title="c3">w</font></span>)</span></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">w</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">w</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">w</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Maroon" title="c3">w</font></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">w</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Maroon" title="c2">z</font></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">w</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="sheffer1.html#D15" title="SHEFFER1:def.15">SHEFFER1:def 15</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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