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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">q</font>, <font color="Olive" title="b2">p</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"><font color="Olive" title="b2">p</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="b2">p</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">p</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="b2">p</font></span>)</span></span>)</span></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">q</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">q</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Olive" title="b1">q</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<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">p</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">q</font>, <font color="Maroon" title="c3">p</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">p</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="c3">p</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">p</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="c3">p</font></span>)</span></span>)</span></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<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">p</font></span><br/>







<a NAME="E1:123"/>
<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">p</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="c3">p</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</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="c3">p</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">p</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="c3">p</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sheffer1.html#D15" title="SHEFFER1:def.15">SHEFFER1:def 15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:123"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">p</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="c3">p</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">p</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="c3">p</font></span>)</span></span>)</span></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<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">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="sheffer2.html#T79" target="_self" title="SHEFFER2:th.79">Th79</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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