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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#L1" title="SHEFFER1:struct.1">ShefferStr</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">L</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  implies <font color="Maroon" title="c1">L</font> is  <a href="sheffer2.html#V1" title="SHEFFER2:attr.1">satisfying_Sh_1</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:2_1_1"/>
<font color="Maroon" title="c1">L</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</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">L</font> is  <a href="sheffer2.html#V1" title="SHEFFER2:attr.1">satisfying_Sh_1</a> </span><br/>

<a NAME="E2:2_1_1"/><span class="kw">then </span>
 for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</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"><font color="Olive" title="b1">x</font> <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="b2">y</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Olive" title="b1">x</font></span>)</span></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">y</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">z</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Olive" title="b1">x</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D10" title="STRUCT_0:def.10">STRUCT_0:def 10</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:2_1_1"/>
<font color="Maroon" title="c1">L</font> is  <a href="sheffer2.html#V1" title="SHEFFER2:attr.1">satisfying_Sh_1</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="sheffer2.html#D1" target="_self" title="SHEFFER2:def.1">Def1</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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